{"title":"A descent basis for the Garsia-Procesi module","authors":"Erik Carlsson, Raymond Chou","doi":"10.1016/j.aim.2024.109945","DOIUrl":"10.1016/j.aim.2024.109945","url":null,"abstract":"<div><p>We assign to each Young diagram <em>λ</em> a subset <span><math><msubsup><mrow><mi>B</mi></mrow><mrow><msup><mrow><mi>λ</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow><mrow><mi>maj</mi></mrow></msubsup></math></span> of the collection of Garsia-Stanton descent monomials, and prove that it determines a basis of the Garsia-Procesi module <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>λ</mi></mrow></msub></math></span>, whose graded character is the Hall-Littlewood polynomial <span><math><msub><mrow><mover><mrow><mi>H</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>λ</mi></mrow></msub><mo>[</mo><mi>X</mi><mo>;</mo><mi>t</mi><mo>]</mo></math></span> <span><span>[14]</span></span>, <span><span>[10]</span></span>, <span><span>[29]</span></span>. This basis is a major index analogue of the basis <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>⊂</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>λ</mi></mrow></msub></math></span> defined by certain recursions, in the same way that the descent basis is related to the Artin basis of the coinvariant algebra <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, which in fact corresponds to the case when <span><math><mi>λ</mi><mo>=</mo><msup><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msup></math></span>. By anti-symmetrizing a subset of this basis with respect to the corresponding Young subgroup under the Springer action, we obtain a basis in the parabolic case, as well as a corresponding formula for the expansion of <span><math><msub><mrow><mover><mrow><mi>H</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>λ</mi></mrow></msub><mo>[</mo><mi>X</mi><mo>;</mo><mi>t</mi><mo>]</mo></math></span>. Despite a similar appearance, it does not appear obvious how to connect the formulas appear to the specialization of the modified Macdonald formula of Haglund, Haiman and Loehr at <span><math><mi>q</mi><mo>=</mo><mn>0</mn></math></span>.</p></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"457 ","pages":"Article 109945"},"PeriodicalIF":1.5,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142240909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Virtual linearity for KPP reaction-diffusion equations","authors":"Andrej Zlatoš","doi":"10.1016/j.aim.2024.109948","DOIUrl":"10.1016/j.aim.2024.109948","url":null,"abstract":"<div><p>We show that long time solution dynamic for general reaction-advection-diffusion equations with KPP reactions is virtually linear in the following sense. Its leading order depends on the non-linear reaction only through its linearization at <span><math><mi>u</mi><mo>=</mo><mn>0</mn></math></span>, and it can also be recovered for general initial data by instead solving the PDE for restrictions of the initial condition to unit cubes on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> (the latter means that non-linear interaction of these restricted solutions has only lower order effects on the overall solution dynamic). The result holds under a uniform bound on the advection coefficient, which we show to be sharp. We also extend it to models with non-local diffusion and KPP reactions.</p></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109948"},"PeriodicalIF":1.5,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142238508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cristina Benea , Frédéric Bernicot , Victor Lie , Marco Vitturi
{"title":"The non-resonant bilinear Hilbert-Carleson operator","authors":"Cristina Benea , Frédéric Bernicot , Victor Lie , Marco Vitturi","doi":"10.1016/j.aim.2024.109939","DOIUrl":"10.1016/j.aim.2024.109939","url":null,"abstract":"<div><p>In this paper we introduce the class of bilinear Hilbert-Carleson operators <span><math><msub><mrow><mo>{</mo><mi>B</mi><msup><mrow><mi>C</mi></mrow><mrow><mi>a</mi></mrow></msup><mo>}</mo></mrow><mrow><mi>a</mi><mo>></mo><mn>0</mn></mrow></msub></math></span> defined by<span><span><span><math><mi>B</mi><msup><mrow><mi>C</mi></mrow><mrow><mi>a</mi></mrow></msup><mo>(</mo><mi>f</mi><mo>,</mo><mi>g</mi><mo>)</mo><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><munder><mi>sup</mi><mrow><mi>λ</mi><mo>∈</mo><mi>R</mi></mrow></munder><mo></mo><mo>|</mo><mo>∫</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>−</mo><mi>t</mi><mo>)</mo><mspace></mspace><mi>g</mi><mo>(</mo><mi>x</mi><mo>+</mo><mi>t</mi><mo>)</mo><mspace></mspace><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mi>λ</mi><msup><mrow><mi>t</mi></mrow><mrow><mi>a</mi></mrow></msup></mrow></msup><mspace></mspace><mfrac><mrow><mi>d</mi><mi>t</mi></mrow><mrow><mi>t</mi></mrow></mfrac><mo>|</mo></math></span></span></span> and show that in the non-resonant case <span><math><mi>a</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>∖</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></math></span> the operator <span><math><mi>B</mi><msup><mrow><mi>C</mi></mrow><mrow><mi>a</mi></mrow></msup></math></span> extends continuously from <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo><mo>×</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo></math></span> into <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>r</mi></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo></math></span> whenever <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mi>p</mi></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>q</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>r</mi></mrow></mfrac></math></span> with <span><math><mn>1</mn><mo><</mo><mi>p</mi><mo>,</mo><mspace></mspace><mi>q</mi><mo>≤</mo><mo>∞</mo></math></span> and <span><math><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mo><</mo><mi>r</mi><mo><</mo><mo>∞</mo></math></span>.</p><p>A key novel feature of these operators is that – in the non-resonant case – <span><math><mi>B</mi><msup><mrow><mi>C</mi></mrow><mrow><mi>a</mi></mrow></msup></math></span> has a <em>hybrid</em> nature enjoying both</p><ul><li><span>(I)</span><span><p><em>zero curvature</em> features inherited from the modulation invariance property of the classical bilinear Hilbert transform (BHT), and</p></span></li><li><span>(II)</span><span><p><em>non-zero curvature</em> features arising from the Carleson-type operator with nonlinear phase <span><math><mi>λ</mi><msup><mrow><mi>t</mi></mrow><mrow><mi>a</mi></mrow></msup></math></span>.</p></span></li></ul> In order to simultaneously control these two competing facets of our operator we develop a <em>two-resolution approach</em>:<ul><li><span>•</span><span><p>A <em>low resolution, multi-scale an","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109939"},"PeriodicalIF":1.5,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142238506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Strong law of large numbers for generalized operator means","authors":"Zoltán Léka , Miklós Pálfia","doi":"10.1016/j.aim.2024.109933","DOIUrl":"10.1016/j.aim.2024.109933","url":null,"abstract":"<div><p>Sturm's strong law of large numbers in <span><math><mrow><mi>CAT</mi></mrow><mo>(</mo><mn>0</mn><mo>)</mo></math></span> spaces and in the Thompson metric space of positive invertible operators is not only an important theoretical generalization of the classical strong law but also serves as a root-finding algorithm in the spirit of a proximal point method with splitting. It provides an easily computable stochastic approximation based on inductive means. The purpose of this paper is to extend Sturm's strong law and its deterministic counterpart, known as the “nodice” version, to unique solutions of nonlinear operator equations that generate exponentially contracting ODE flows in the Thompson metric. This includes a broad family of so-called generalized (Karcher) operator means introduced by Pálfia in 2016. The setting of the paper also covers the framework of order-preserving flows on Thompson metric spaces, as investigated by Gaubert and Qu in 2014, and provides a generally applicable resolvent theory for this setting.</p></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"457 ","pages":"Article 109933"},"PeriodicalIF":1.5,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0001870824004481/pdfft?md5=d3a3a3dd73c6f07b12612b0683cffa2d&pid=1-s2.0-S0001870824004481-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142173008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Subspace concentration of zonoids and a sharp Minkowski mixed volume inequality","authors":"Qiang Sun, Ge Xiong","doi":"10.1016/j.aim.2024.109934","DOIUrl":"10.1016/j.aim.2024.109934","url":null,"abstract":"<div><p>The mixed volume measure <span><math><msub><mrow><mi>V</mi></mrow><mrow><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></msub></math></span> of compact convex sets <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> is the localization of the classic Minkowski mixed volume <span><math><mi>V</mi><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span> and is one of the generalizations of the important cone-volume measure. When <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></math></span> are zonotopes and <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> is a convex body or <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> are zonoids in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, the subspace concentration of <span><math><msub><mrow><mi>V</mi></mrow><mrow><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></msub></math></span> is proved. As applications, a subspace concentration phenomenon for quermassintegrals is revealed and a sharp affine isoperimetric inequality for the Minkowski mixed volume is established.</p></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"457 ","pages":"Article 109934"},"PeriodicalIF":1.5,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142168327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Density of exponentials and Perron-Frobenius operators","authors":"Somnath Ghosh , Debkumar Giri","doi":"10.1016/j.aim.2024.109932","DOIUrl":"10.1016/j.aim.2024.109932","url":null,"abstract":"<div><p>In this article, we study the weak-star density of the linear span of the trigonometric functions<span><span><span><math><mrow><mo>{</mo><msub><mrow><mi>e</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>n</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>π</mi><mi>i</mi><mo>(</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>n</mi><mi>y</mi><mo>)</mo></mrow></msup><mo>,</mo><mspace></mspace><msubsup><mrow><mi>e</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>n</mi></mrow><mrow><mo><</mo><mi>β</mi><mo>></mo></mrow></msubsup><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>π</mi><mi>i</mi><mi>β</mi><mo>(</mo><mi>m</mi><mo>/</mo><mi>x</mi><mo>+</mo><mi>n</mi><mo>/</mo><mi>y</mi><mo>)</mo></mrow></msup><mo>;</mo><mspace></mspace></mrow><mspace></mspace><mrow><mspace></mspace><mi>m</mi><mo>,</mo><mi>n</mi><mo>∈</mo><mi>Z</mi><mo>}</mo></mrow></math></span></span></span> for a positive real <em>β</em>. We aim to extend the results of Hedenmalm and Montes-Rodríguez (2011) <span><span>[18]</span></span> and Canto-Martín, Hedenmalm, and Montes-Rodríguez (2014) <span><span>[8]</span></span> in the plane. They have extensively studied the weak-star completeness of the <em>hyperbolic trigonometric system</em> in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo></math></span>. This is the dual formulation of the Heisenberg uniqueness pair for (hyperbola, certain lattice-cross).</p><p>As in their work, <span><math><mi>β</mi><mo>=</mo><mn>1</mn></math></span> turns out to be the critical value. In particular, one of our main results asserts that the space spanned by the aforesaid trigonometric functions is weak-star dense in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> of the set <span><math><msub><mrow><mi>Θ</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>β</mi></mrow></msub><mo>=</mo><msup><mrow><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>∪</mo><msup><mrow><mo>(</mo><mi>R</mi><mo>∖</mo><mo>(</mo><mo>−</mo><mi>β</mi><mo>,</mo><mi>β</mi><mo>]</mo><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span> if and only if <span><math><mn>0</mn><mo><</mo><mi>β</mi><mo>≤</mo><mn>1</mn></math></span>, and the corresponding pre-annihilator space has finite dimension whenever <span><math><mi>β</mi><mo>></mo><mn>1</mn></math></span>. However, for <span><math><mi>β</mi><mo>></mo><mn>1</mn></math></span>, the pre-annihilator space can be made infinite-dimensional by allowing functions with slightly bigger support than <span><math><msub><mrow><mi>Θ</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>β</mi></mrow></msub></math></span>. To be precise, let <span><math><msubsup><mrow><mi>Θ</mi></mrow><mrow><mi>β</mi></mrow><mrow><mo>″</mo></mrow></msubsup><mo>⊆</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>∖</mo","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"457 ","pages":"Article 109932"},"PeriodicalIF":1.5,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142168328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Regularizable collinear periodic solutions in the n-body problem with arbitrary masses","authors":"Guowei Yu","doi":"10.1016/j.aim.2024.109947","DOIUrl":"10.1016/j.aim.2024.109947","url":null,"abstract":"<div><p>For <em>n</em>-body problem with arbitrary positive masses, we prove there are regularizable collinear periodic solutions for any ordering of the masses, going from a simultaneous binary collision to another in half of a period with half of the masses moving monotonically to the right and the other half monotonically to the left. When the masses satisfy certain equality condition, the solutions have extra symmetry. This also gives a new proof of the existence of Schubart orbit, when <span><math><mi>n</mi><mo>=</mo><mn>3</mn></math></span>.</p></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"457 ","pages":"Article 109947"},"PeriodicalIF":1.5,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142168418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The average number of integral points on the congruent number curves","authors":"Stephanie Chan","doi":"10.1016/j.aim.2024.109946","DOIUrl":"10.1016/j.aim.2024.109946","url":null,"abstract":"<div><p>We show that the total number of non-torsion integral points on the elliptic curves <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>D</mi></mrow></msub><mo>:</mo><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>−</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>x</mi></math></span>, where <em>D</em> ranges over positive squarefree integers less than <em>N</em>, is <span><math><mi>O</mi><mo>(</mo><mi>N</mi><msup><mrow><mo>(</mo><mi>log</mi><mo></mo><mi>N</mi><mo>)</mo></mrow><mrow><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>+</mo><mi>ϵ</mi></mrow></msup><mo>)</mo></math></span>. The proof involves a discriminant-lowering procedure on integral binary quartic forms and an application of Heath-Brown's method on estimating the average size of the 2-Selmer groups of the curves in this family.</p></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"457 ","pages":"Article 109946"},"PeriodicalIF":1.5,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0001870824004614/pdfft?md5=e61e01dc3d1a09b4e1bf01af1246df6b&pid=1-s2.0-S0001870824004614-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142168326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dynamical classification of analytic one-frequency quasi-periodic SO(3,R)-cocycles","authors":"Xuanji Hou , Yi Pan , Qi Zhou","doi":"10.1016/j.aim.2024.109943","DOIUrl":"10.1016/j.aim.2024.109943","url":null,"abstract":"<div><p>We establish a close connection between acceleration and dynamical degree for one-frequency quasi-periodic compact cocycles, by showing that two vectors derived separately from each coincide. Based on this, we provide a dynamical classification of one-frequency quasi-periodic <span><math><mrow><mi>SO</mi></mrow><mo>(</mo><mn>3</mn><mo>,</mo><mi>R</mi><mo>)</mo></math></span>-cocycles.</p></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"457 ","pages":"Article 109943"},"PeriodicalIF":1.5,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0001870824004584/pdfft?md5=0083bfa17c98a2af5ca3df7ab4ea8b19&pid=1-s2.0-S0001870824004584-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142168329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Finite sets containing zero are mapping degree sets","authors":"Cristina Costoya , Vicente Muñoz , Antonio Viruel","doi":"10.1016/j.aim.2024.109942","DOIUrl":"10.1016/j.aim.2024.109942","url":null,"abstract":"<div><p>In this paper we solve in the positive the question of whether any finite set of integers, containing 0, is the mapping degree set between two oriented closed connected manifolds of the same dimension. We extend this question to the rational setting, where an affirmative answer is also given.</p></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"457 ","pages":"Article 109942"},"PeriodicalIF":1.5,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0001870824004572/pdfft?md5=ef51c4901c7fe1d7dbb8717264ee2948&pid=1-s2.0-S0001870824004572-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142168330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
