Journal of the London Mathematical Society-Second Series最新文献_第4页

Arithmetic degree and its application to Zariski dense orbit conjecture 算术度及其在Zariski稠密轨道猜想中的应用

IF 1.2 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-09 DOI: 10.1112/jlms.70282

Yohsuke Matsuzawa, Junyi Xie

{"title":"Arithmetic degree and its application to Zariski dense orbit conjecture","authors":"Yohsuke Matsuzawa, Junyi Xie","doi":"10.1112/jlms.70282","DOIUrl":"10.1112/jlms.70282","url":null,"abstract":"We prove that for a dominant rational self-map <math>\u0000 <semantics>\u0000 <mi>f</mi>\u0000 <annotation>$f$</annotation>\u0000 </semantics></math> on a quasi-projective variety defined over <math>\u0000 <semantics>\u0000 <mover>\u0000 <mi>Q</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 <annotation>$overline{mathbb {Q}}$</annotation>\u0000 </semantics></math>, there is a point whose <math>\u0000 <semantics>\u0000 <mi>f</mi>\u0000 <annotation>$f$</annotation>\u0000 </semantics></math>-orbit is well-defined and its arithmetic degree is arbitrarily close to the first dynamical degree of <math>\u0000 <semantics>\u0000 <mi>f</mi>\u0000 <annotation>$f$</annotation>\u0000 </semantics></math>. As an application, we prove that Zariski dense orbit conjecture holds for a birational map defined over <math>\u0000 <semantics>\u0000 <mover>\u0000 <mi>Q</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 <annotation>$overline{mathbb {Q}}$</annotation>\u0000 </semantics></math> whose first dynamical degree is strictly larger than its third dynamical degree. In particular, the conjecture holds for birational maps on threefolds whose first dynamical is degree greater than 1.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145012730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Affine and cyclotomic webs 仿射和切环网

IF 1.2 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-08 DOI: 10.1112/jlms.70278

Linliang Song, Weiqiang Wang

{"title":"Affine and cyclotomic webs","authors":"Linliang Song, Weiqiang Wang","doi":"10.1112/jlms.70278","DOIUrl":"10.1112/jlms.70278","url":null,"abstract":"Generalizing the polynomial web category, we introduce a diagrammatic <math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$mathbb {k}$</annotation>\u0000 </semantics></math>-linear monoidal category, the affine web category, for any commutative ring <math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$mathbb {k}$</annotation>\u0000 </semantics></math>. Integral bases consisting of elementary diagrams are obtained for the affine web category and its cyclotomic quotient categories. Connections between cyclotomic web categories and finite <math>\u0000 <semantics>\u0000 <mi>W</mi>\u0000 <annotation>$W$</annotation>\u0000 </semantics></math>-algebras are established, leading to a diagrammatic presentation of idempotent subalgebras of <math>\u0000 <semantics>\u0000 <mi>W</mi>\u0000 <annotation>$W$</annotation>\u0000 </semantics></math>-Schur algebras introduced by Brundan–Kleshchev. The affine web category will be used as a basic building block of another <math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$mathbb {k}$</annotation>\u0000 </semantics></math>-linear monoidal category, the affine Schur category, formulated in a sequel.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145012131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On fixed-point-free involutions in actions of finite exceptional groups of Lie type 李型有限例外群作用的不动点自由对合

IF 1.2 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-08 DOI: 10.1112/jlms.70263

Timothy C. Burness, Mikko Korhonen

{"title":"On fixed-point-free involutions in actions of finite exceptional groups of Lie type","authors":"Timothy C. Burness, Mikko Korhonen","doi":"10.1112/jlms.70263","DOIUrl":"10.1112/jlms.70263","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> be a nontrivial transitive permutation group on a finite set <math>\u0000 <semantics>\u0000 <mi>Ω</mi>\u0000 <annotation>$Omega$</annotation>\u0000 </semantics></math>. By a classical theorem of Jordan, <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> contains a derangement, which is an element with no fixed points on <math>\u0000 <semantics>\u0000 <mi>Ω</mi>\u0000 <annotation>$Omega$</annotation>\u0000 </semantics></math>. Given a prime divisor <math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math> of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 <mi>Ω</mi>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 <annotation>$|Omega |$</annotation>\u0000 </semantics></math>, we say that <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> is <math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math>-elusive if it does not contain a derangement of order <math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math>. In a paper from 2011, Burness, Giudici, and Wilson essentially reduce the classification of the <math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math>-elusive primitive groups to the case where <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> is an almost simple group of Lie type. The classical groups with an <math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math>-elusive socle have been determined by Burness and Giudici, and in this paper, we consider the analogous problem for the exceptional groups of Lie type, focussing on the special case <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$r=2$</annotation>\u0000 </semantics></math>. Our main theorem describes all the ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70263","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145012206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Taking limits in topological recursion 在拓扑递归中求极限

IF 1.2 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-04 DOI: 10.1112/jlms.70286

Gaëtan Borot, Vincent Bouchard, Nitin Kumar Chidambaram, Reinier Kramer, Sergey Shadrin

{"title":"Taking limits in topological recursion","authors":"Gaëtan Borot, Vincent Bouchard, Nitin Kumar Chidambaram, Reinier Kramer, Sergey Shadrin","doi":"10.1112/jlms.70286","DOIUrl":"10.1112/jlms.70286","url":null,"abstract":"When does topological recursion applied to a family of spectral curves commute with taking limits? This problem is subtle, especially when the ramification structure of the spectral curve changes at the limit point. We provide sufficient (straightforward-to-use) conditions for checking when the commutation with limits holds, thereby closing a gap in the literature where this compatibility has been used several times without justification. This takes the form of a stronger result of analyticity of the topological recursion along suitable families. To tackle this question, we formalise the notion of global topological recursion and provide sufficient conditions for its equivalence with local topological recursion. The global version facilitates the study of analyticity and limits. For non-degenerate algebraic curves, we reformulate these conditions purely in terms of the structure of its underlying singularities. Finally, we apply this to study deformations of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>r</mi>\u0000 <mo>,</mo>\u0000 <mi>s</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$ (r,s)$</annotation>\u0000 </semantics></math>-spectral curves, spectral curves for weighted Hurwitz numbers and provide several other examples and non-examples (where the commutation with limits fails).","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70286","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Entire functions with Cantor bouquet Julia sets 整个功能与康托花束Julia集

IF 1.2 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-03 DOI: 10.1112/jlms.70142

Leticia Pardo-Simón, Lasse Rempe

{"title":"Entire functions with Cantor bouquet Julia sets","authors":"Leticia Pardo-Simón, Lasse Rempe","doi":"10.1112/jlms.70142","DOIUrl":"10.1112/jlms.70142","url":null,"abstract":"A hyperbolic transcendental entire function with connected Fatou set is said to be of disjoint type. It is known that the Julia set of a disjoint-type function of finite order is a Cantor bouquet; in particular, it is a collection of arcs (‘hairs'), each connecting a finite endpoint to infinity. We show that the latter property is equivalent to the function being criniferous in the sense of Benini and Rempe (a necessary condition for having a Cantor bouquet Julia set). On the other hand, we show that there is a criniferous disjoint-type entire function whose Julia set is not a Cantor bouquet. We also provide a new characterisation of Cantor bouquet Julia sets in terms of the existence of certain absorbing sets for the set of escaping points, and use this to give a new intrinsic description of a class of entire functions previously introduced by the first author. Finally, the main known sufficient condition for Cantor bouquet Julia sets is the so-called head-start condition of Rottenfußer et al. Under a mild geometric assumption, we prove that this condition is also necessary.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70142","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dichotomy laws for the Hausdorff measure of shrinking target sets in β $beta$ -dynamical systems β $ β $ -动力系统中收缩目标集的Hausdorff测度的二分律

IF 1.2 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-03 DOI: 10.1112/jlms.70284

Yubin He

引用次数: 0

Geometric realizations of the s-weak order and its lattice quotients s-弱阶及其格商的几何实现

IF 1.2 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-03 DOI: 10.1112/jlms.70268

Eva Philippe, Vincent Pilaud

{"title":"Geometric realizations of the s-weak order and its lattice quotients","authors":"Eva Philippe, Vincent Pilaud","doi":"10.1112/jlms.70268","DOIUrl":"10.1112/jlms.70268","url":null,"abstract":"For an <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-tuple <math>\u0000 <semantics>\u0000 <mi>s</mi>\u0000 <annotation>${bm{s}}$</annotation>\u0000 </semantics></math> of nonnegative integers, the <math>\u0000 <semantics>\u0000 <mi>s</mi>\u0000 <annotation>${bm{s}}$</annotation>\u0000 </semantics></math>-weak order is a lattice structure on <math>\u0000 <semantics>\u0000 <mi>s</mi>\u0000 <annotation>${bm{s}}$</annotation>\u0000 </semantics></math>-trees, generalizing the weak order on permutations. We first describe the join irreducible elements, the canonical join representations, and the forcing order of the <math>\u0000 <semantics>\u0000 <mi>s</mi>\u0000 <annotation>${bm{s}}$</annotation>\u0000 </semantics></math>-weak order in terms of combinatorial objects, generalizing the arcs, the noncrossing arc diagrams, and the subarc order for the weak order. We then extend the theory of shards and shard polytopes to construct geometric realizations of the <math>\u0000 <semantics>\u0000 <mi>s</mi>\u0000 <annotation>${bm{s}}$</annotation>\u0000 </semantics></math>-weak order and all its lattice quotients as polyhedral complexes, generalizing the quotient fans and quotientopes of the weak order.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70268","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On 3-graphs with vanishing codegree Turán density 在余度消失的3图上Turán密度

IF 1.2 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-03 DOI: 10.1112/jlms.70281

Laihao Ding, Ander Lamaison, Hong Liu, Shuaichao Wang, Haotian Yang

{"title":"On 3-graphs with vanishing codegree Turán density","authors":"Laihao Ding, Ander Lamaison, Hong Liu, Shuaichao Wang, Haotian Yang","doi":"10.1112/jlms.70281","DOIUrl":"10.1112/jlms.70281","url":null,"abstract":"For a <math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>-uniform hypergraph (or simply <math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>-graph) <math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>, the codegree Turán density <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>π</mi>\u0000 <mi>co</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>F</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$pi _{mathrm{co}}(F)$</annotation>\u0000 </semantics></math> is the supremum over all <math>\u0000 <semantics>\u0000 <mi>α</mi>\u0000 <annotation>$alpha$</annotation>\u0000 </semantics></math> such that there exist arbitrarily large <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-vertex <math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-free <math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>-graphs <math>\u0000 <semantics>\u0000 <mi>H</mi>\u0000 <annotation>$H$</annotation>\u0000 </semantics></math> in which every <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>k</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(k-1)$</annotation>\u0000 </semantics></math>-subset of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>V</mi>\u0000 <mo>(</mo>\u0000 <mi>H</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$V(H)$</annotation>\u0000 </semantics></math> is contained in at least <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$alpha n$</annotation>\u0000 </semantics></math> edges. In this paper, we study the problem of what 3-graphs <math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math> satisfy <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>π</mi>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Deformations of Anosov subgroups: Limit cones and growth indicators Anosov亚群的变形：极限锥和生长指标

IF 1.2 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-02 DOI: 10.1112/jlms.70280

Subhadip Dey, Hee Oh

引用次数: 0

Interactions between universal composition operators and complex dynamics 通用复合算子与复杂动力学之间的相互作用

IF 1.2 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-08-28 DOI: 10.1112/jlms.70262

Vasiliki Evdoridou, Clifford Gilmore, Myrto Manolaki

{"title":"Interactions between universal composition operators and complex dynamics","authors":"Vasiliki Evdoridou, Clifford Gilmore, Myrto Manolaki","doi":"10.1112/jlms.70262","DOIUrl":"10.1112/jlms.70262","url":null,"abstract":"This paper is concerned with universality properties of composition operators <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mi>f</mi>\u0000 </msub>\u0000 <annotation>$C_f$</annotation>\u0000 </semantics></math>, where the symbol <math>\u0000 <semantics>\u0000 <mi>f</mi>\u0000 <annotation>$f$</annotation>\u0000 </semantics></math> is given by a transcendental entire function restricted to parts of its Fatou set. We determine universality of <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mi>f</mi>\u0000 </msub>\u0000 <annotation>$C_f$</annotation>\u0000 </semantics></math> when <math>\u0000 <semantics>\u0000 <mi>f</mi>\u0000 <annotation>$f$</annotation>\u0000 </semantics></math> is restricted to (subsets of) Baker and wandering domains. We then describe the behaviour of universal vectors, under the action of iterates of the symbol <math>\u0000 <semantics>\u0000 <mi>f</mi>\u0000 <annotation>$f$</annotation>\u0000 </semantics></math>, near periodic points of <math>\u0000 <semantics>\u0000 <mi>f</mi>\u0000 <annotation>$f$</annotation>\u0000 </semantics></math> or near infinity. Finally, we establish a principal universality theorem for the more general class of weighted composition operators, which we then apply to uncover universality results in the context of various types of Fatou components of the associated symbol.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70262","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144914892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0