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On Which Closed Nonorientable Surfaces Do Pseudo-Anosov Homeomorphisms Exist? 在哪些闭合非定向曲面上存在伪anosov同胚？
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-06-15 DOI: 10.1134/S1560354726520011
Anatoly A. Medvedev
{"title":"On Which Closed Nonorientable Surfaces Do Pseudo-Anosov Homeomorphisms Exist?","authors":"Anatoly A. Medvedev","doi":"10.1134/S1560354726520011","DOIUrl":"10.1134/S1560354726520011","url":null,"abstract":"<div><p>In this paper, we provide a complete answer to the question posed in its title. For all closed surfaces for which this question has not yet been resolved, namely, closed nonorientable surfaces of odd genus greater than 5, a series of examples of pseudo-Anosov homeomorphisms are constructed. Each of these homeomorphisms is defined by\u0000means of the so-called code, which implies using the construction of a band surface. Combined with previously obtained results, this allows us to fill in the gap and to formulate a general result: pseudo-Anosov homeomorphisms exist on a closed nonorientable surface if and only if its genus is at least 4.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 4","pages":"503 - 517"},"PeriodicalIF":0.8,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
2-Elliptic Periodic Orbits near a Nonsimple Homoclinic Tangency inFour-Dimensional Symplectic Maps 非简单同斜切四维辛映射附近的2-椭圆周期轨道
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-05-28 DOI: 10.1134/S1560354726030019
Sergey Gonchenko, Lev Lerman, Dmitry Turaev
{"title":"2-Elliptic Periodic Orbits near a Nonsimple Homoclinic Tangency in\u0000Four-Dimensional Symplectic Maps","authors":"Sergey Gonchenko,&nbsp;Lev Lerman,&nbsp;Dmitry Turaev","doi":"10.1134/S1560354726030019","DOIUrl":"10.1134/S1560354726030019","url":null,"abstract":"<div><p>We show that bifurcations of four-dimensional symplectic diffeomorphisms with a quadratic homoclinic tangency to a saddle periodic orbit with real multipliers produce 2-elliptic periodic orbits if the tangency is not partially hyperbolic. We show that a normal form for the rescaled first-return maps near such tangency is given by a four-dimensional symplectic Hénon-like map and study bifurcations of the first-return maps in generic two-parameter families.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 3","pages":"349 - 369"},"PeriodicalIF":0.8,"publicationDate":"2026-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148060952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Erratum to: Nonsingular Flows with a Twisted Saddle Orbit on Orientable 3-Manifolds 可定向3流形上具有扭曲鞍形轨道的非奇异流的勘误
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-05-28 DOI: 10.1134/S1560354726030020
Olga V. Pochinka, Danila D. Shubin
{"title":"Erratum to: Nonsingular Flows with a Twisted Saddle Orbit on Orientable 3-Manifolds","authors":"Olga V. Pochinka,&nbsp;Danila D. Shubin","doi":"10.1134/S1560354726030020","DOIUrl":"10.1134/S1560354726030020","url":null,"abstract":"","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 3","pages":"502 - 502"},"PeriodicalIF":0.8,"publicationDate":"2026-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148060951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 a Novel Hamiltonian Description of the Nonholonomic Suslov Problem 非完整Suslov问题的一种新颖哈密顿描述
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-04-07 DOI: 10.1134/S1560354726020048
Andrey V. Tsiganov
{"title":"On a Novel Hamiltonian Description of the Nonholonomic Suslov Problem","authors":"Andrey V. Tsiganov","doi":"10.1134/S1560354726020048","DOIUrl":"10.1134/S1560354726020048","url":null,"abstract":"<div><p>We present some new Poisson bivectors that are invariants by the flow of the nonholonomic Suslov problem.\u0000Two rank-four invariant Poisson bivectors have globally defined Casimir functions and, therefore, define cubic Poisson brackets of the five-dimensional state space with standard symplectic leaves. For the Suslov gyrostat in the potential field we found rank-two Poisson bivectors having only two globally defined Casimir functions and, therefore, we say about formal Hamiltonian description in these cases.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"263 - 272"},"PeriodicalIF":0.8,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147637003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Abnormal Geodesics for a Carnot Group with Growth Vector ((2,3,5,8,14)) 带生长向量的卡诺群的异常测地线 ((2,3,5,8,14))
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-04-07 DOI: 10.1134/S1560354726020012
Alexander A. Kilin, Andrzej J. Maciejewski, Ivan S. Mamaev, Maria Przybylska, Yuri L. Sachkov
{"title":"Abnormal Geodesics for a Carnot Group with Growth Vector ((2,3,5,8,14))","authors":"Alexander A. Kilin,&nbsp;Andrzej J. Maciejewski,&nbsp;Ivan S. Mamaev,&nbsp;Maria Przybylska,&nbsp;Yuri L. Sachkov","doi":"10.1134/S1560354726020012","DOIUrl":"10.1134/S1560354726020012","url":null,"abstract":"<div><p>This paper is concerned with abnormal geodesics on the Carnot group with growth vector <span>((2,3,5,8,14))</span>. Because of a large number of symmetries, this problem reduces to an analysis of the five-dimensional flow. Using the Kovalevskaya method, integrable cases of the resulting system are identified. For these cases, first integrals and explicit solutions are found. It is shown that in the general case the system admits no additional meromorphic first integrals. The paper concludes by discussing some problems regarding the abnormal geodesics on Lie groups.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"177 - 224"},"PeriodicalIF":0.8,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147637004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Spectral Analysis of a System of Pendula Hanging from a Viscoelastic String and of its Synchronization Patterns 粘弹性弦垂摆系统及其同步模式的频谱分析
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-04-07 DOI: 10.1134/S1560354726020061
Francesco Fassò, Sara Galasso
{"title":"Spectral Analysis of a System of Pendula Hanging from a Viscoelastic String and of its Synchronization Patterns","authors":"Francesco Fassò,&nbsp;Sara Galasso","doi":"10.1134/S1560354726020061","DOIUrl":"10.1134/S1560354726020061","url":null,"abstract":"<div><p>We propose and study a model for the mechanical system constituted by\u0000a chain of <span>(ngeqslant 1)</span> identical pendula hanging from a viscoelastic\u0000string with fixed extrema. The novelty of our approach is to\u0000describe the string as a continuous system, specifically, as a\u0000one-dimensional viscoelastic Kelvin – Voigt string. The resulting\u0000system is a hybrid nonlinear system of coupled PDEs and ODEs. We\u0000linearize the system around the attractive equilibrium with pendula\u0000and string pointing downwards. The (infinite-dimensional)\u0000linearization decouples into a “vertical” and a “horizontal”\u0000subsystems. The former is a viscoelastic version of the well known\u0000Rayleigh loaded string, and its point spectrum is known. We thus\u0000consider the latter, which describes, at the linear level, the\u0000horizontal oscillations of string and pendula. We obtain closed form\u0000expressions for the eigenvalue equations and for the eigenfunctions\u0000for any value of <span>(n)</span>. Next, we study the point spectrum with a\u0000combination of analytical and numerical techniques, adopting a\u0000continuation approach from the limiting cases of massless pendula, which\u0000involves the well known spectrum of the Kelvin – Voigt string. Finally,\u0000we focus on the identification, particularly when <span>(n=2)</span> and as a\u0000function of the parameters, of the eigenvalues closest to the\u0000imaginary axis, whose eigenfunction(s) dominate the asymptotic\u0000dynamics of the (horizontal) linearized systems and can explain the\u0000appearance of synchronization patterns in the chain of pendula.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"290 - 335"},"PeriodicalIF":0.8,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147637008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Towards a Classification of Toric and Semitoric Singular Symplectic Manifolds 关于环半奇异辛流形的分类
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-04-07 DOI: 10.1134/S1560354726020036
Eva Miranda
{"title":"Towards a Classification of Toric and Semitoric Singular Symplectic Manifolds","authors":"Eva Miranda","doi":"10.1134/S1560354726020036","DOIUrl":"10.1134/S1560354726020036","url":null,"abstract":"<div><p>In this article, we present a classification of toric <span>(b^{m})</span>-symplectic manifolds and outline a program for the classification of semitoric singular symplectic manifolds. As a testing ground, we begin with the case of <span>(b)</span>-symplectic manifolds, where a Delzant-type theorem for toric actions has already been established [13]. Building on this foundation, we extend the framework to the broader setting of <span>(b^{m})</span>-symplectic manifolds, thereby establishing the first classification result for <span>(b^{m})</span>-toric manifolds. This achievement lays the groundwork for a conjectural classification theory of semitoric systems in dimension four on <span>(b^{m})</span>-symplectic manifolds. Furthermore, by employing the reduction theory developed in [21], we propose a conjectural classification scheme for higher-dimensional semitoric manifolds, aiming to generalize the Pelayo – Vũ Ngọc classification program [32, 33] to the singular <span>(b^{m})</span>-setting.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"240 - 262"},"PeriodicalIF":0.8,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Dynamics of a Body with a Trailing Edge and Embedded Dipoles in an Ideal Fluid 理想流体中带后缘和嵌入偶极体的动力学
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-04-07 DOI: 10.1134/S1560354726020024
Stefan G. Llewellyn Smith, Sean D. Peterson
{"title":"Dynamics of a Body with a Trailing Edge and Embedded Dipoles in an Ideal Fluid","authors":"Stefan G. Llewellyn Smith,&nbsp;Sean D. Peterson","doi":"10.1134/S1560354726020024","DOIUrl":"10.1134/S1560354726020024","url":null,"abstract":"<div><p>Equations of motion for a body moving through an ideal fluid when the flow is irrotational and incompressible are obtained taking account of embedded dipoles on the boundary and the Kutta – Chaplygin condition. We develop the embedded dipole model from the complex potential of a dipole on the boundary of a body, oriented so as to preserve no-penetration through the body, using a conformal mapping approach. The resulting hydrodynamic force and moment on the body depend on the dipoles’ strength and position along the body. Using the flat plate as a model geometry, we examine the evolution of the resulting system under the conditions of fixed and time-varying circulation with and without embedded dipoles. We assume two embedded dipoles symmetrically positioned about the center point of the plate, finding that the presence of the dipoles reduces the fluctuations of the angle of attack of the plate. We explore conserved quantities for the system and perform a linear stability analysis, which leads to a constraint on the dipole strength for stability of a plate moving at zero angle of attack with either circulation equal to zero or the Kutta – Chaplygin condition applied.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"225 - 239"},"PeriodicalIF":0.8,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147637006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Discrete Mechanics and Nonholonomic Integrators 离散力学与非完整积分器
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-04-07 DOI: 10.1134/S156035472602005X
Dmitry V. Zenkov
{"title":"Discrete Mechanics and Nonholonomic Integrators","authors":"Dmitry V. Zenkov","doi":"10.1134/S156035472602005X","DOIUrl":"10.1134/S156035472602005X","url":null,"abstract":"<div><p>Nonholonomic systems are mechanical systems with ideal linear velocity constraints that are not derivable from position constraints and with dynamics identified by the Lagrange – d’Alembert principle.\u0000This paper surveys discrete-time nonholonomic mechanics with applications to numerical integration of nonholonomic systems.\u0000This includes an exposition of key elements of discrete mechanics, discrete Lagrange – d’Alembert principle, and exact nonholonomic integrators on vector spaces.\u0000Exact variational integrators were introduced and exposed in the context of Lagrangian mechanics by Marsden and West.\u0000These integrators sample the trajectories of mechanical systems and are useful for developing practical mechanical integrators.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 Editors:","pages":"273 - 289"},"PeriodicalIF":0.8,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147637007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 the Novikov Problem for Superposition of Periodic Potentials 周期势叠加的Novikov问题
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2026-02-27 DOI: 10.1134/S1560354726510027
Andrey Ya. Maltsev
{"title":"On the Novikov Problem for Superposition of Periodic Potentials","authors":"Andrey Ya. Maltsev","doi":"10.1134/S1560354726510027","DOIUrl":"10.1134/S1560354726510027","url":null,"abstract":"<div><p>We consider the Novikov problem, namely, the problem of describing\u0000the global geometry of level lines of quasiperiodic functions on a plane,\u0000for a special class of two-dimensional potentials. Potentials of this\u0000class play an important role in the physics of two-dimensional systems\u0000and are defined by superpositions of two periodic potentials with\u0000the same rotational symmetry. For different orientations of the periods\u0000of the original potentials, the resulting potential can have 4 quasiperiodes\u0000or be periodic. The main result of the paper is a proof that quasiperiodic\u0000potentials of this class can have open level lines at only one energy level.\u0000This property brings these potentials closer to random potentials on a plane,\u0000as well as to potentials with 3 quasiperiodes possessing “chaotic” level lines.\u0000The paper also presents an estimate for the energy interval containing open\u0000level lines of periodic potentials arising at “magic” angles of rotation\u0000of the original potentials relative to each other.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 4","pages":"632 - 667"},"PeriodicalIF":0.8,"publicationDate":"2026-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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