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Regular and Chaotic Dynamics最新文献

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Singular Points in Generic Two-Parameter Families of Vector Fields on a 2-Manifold 双平面上通用双参数矢量场族中的奇异点
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-04-07 DOI: 10.1134/S1560354725020066
Dmitry A. Filimonov, Yulij S. Ilyashenko
{"title":"Singular Points in Generic Two-Parameter Families of Vector Fields on a 2-Manifold","authors":"Dmitry A. Filimonov,&nbsp;Yulij S. Ilyashenko","doi":"10.1134/S1560354725020066","DOIUrl":"10.1134/S1560354725020066","url":null,"abstract":"<div><p>In this paper, we give a full description of all possible singular points that occur in generic 2-parameter families of vector fields on compact 2-manifolds. This is a part of a large project aimed at a complete study of global bifurcations in two-parameter families of vector fields on the two-sphere.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 2","pages":"279 - 290"},"PeriodicalIF":0.8,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793151","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
A Geometric Model for Pseudohyperbolic Shilnikov Attractors 伪双曲希尔尼科夫吸引力的几何模型
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-04-07 DOI: 10.1134/S1560354725020029
Dmitry Turaev
{"title":"A Geometric Model for Pseudohyperbolic Shilnikov Attractors","authors":"Dmitry Turaev","doi":"10.1134/S1560354725020029","DOIUrl":"10.1134/S1560354725020029","url":null,"abstract":"<div><p>We describe a <span>(C^{1})</span>-open set of systems of differential equations in <span>(R^{n})</span>, for any <span>(ngeqslant 4)</span>, where every system has a chain-transitive chaotic attractor which\u0000contains a saddle-focus equilibrium with a two-dimensional unstable manifold. The attractor also includes a wild hyperbolic set and a heterodimensional cycle involving\u0000hyperbolic sets with different numbers of positive Lyapunov exponents.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 2","pages":"174 - 187"},"PeriodicalIF":0.8,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S1560354725020029.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Topological Classification of Polar Flows on Four-Dimensional Manifolds 四维漫域上极性流的拓扑分类
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-04-07 DOI: 10.1134/S1560354725020054
Elena Ya. Gurevich, Ilya A. Saraev
{"title":"Topological Classification of Polar Flows on Four-Dimensional Manifolds","authors":"Elena Ya. Gurevich,&nbsp;Ilya A. Saraev","doi":"10.1134/S1560354725020054","DOIUrl":"10.1134/S1560354725020054","url":null,"abstract":"<div><p>S. Smale has shown that any closed smooth manifold admits a gradient-like flow, which is a structurally stable flow with a finite nonwandering set. Polar flows form a subclass of gradient-like flows characterized by the simplest nonwandering set for the given manifold, consisting of exactly one source, one sink, and a finite number of saddle equilibria. We describe the topology of four-dimensional closed manifolds that admit polar flows without heteroclinic intersections, as well as all classes of topological equivalence of polar flows on each manifold. In particular, we demonstrate that there exists a countable set of nonequivalent flows with a given number <span>(kgeqslant 2)</span> of saddle equilibria on each manifold, which contrasts with the situation in lower-dimensional analogues.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 2","pages":"254 - 278"},"PeriodicalIF":0.8,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793157","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 Morse – Smale 3-Diffeomorphisms with a Given Tuple of Sink Points Periods 关于莫尔斯-斯马尔 3-二非定常与给定汇点周期元组
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-04-07 DOI: 10.1134/S1560354725020042
Marina K. Barinova, Evgenii M. Osenkov, Olga V. Pochinka
{"title":"On Morse – Smale 3-Diffeomorphisms with a Given Tuple of Sink Points Periods","authors":"Marina K. Barinova,&nbsp;Evgenii M. Osenkov,&nbsp;Olga V. Pochinka","doi":"10.1134/S1560354725020042","DOIUrl":"10.1134/S1560354725020042","url":null,"abstract":"<div><p>In investigating dynamical systems with chaotic attractors, many aspects of global behavior of a flow or a diffeomorphism with such an attractor are studied by replacing a nontrivial attractor by a trivial one [1, 2, 11, 14].\u0000Such a method allows one to reduce the original system to a regular system, for instance, of a Morse – Smale system, matched with it. In most cases, the possibility of such a substitution is justified by the existence of Morse – Smale diffeomorphisms with partially determined periodic data, the complete understanding of their dynamics and the topology of manifolds, on which they are defined. With this aim in mind, we consider Morse – Smale diffeomorphisms <span>(f)</span> with determined periods of the sink points, given on a closed smooth 3-manifold. We have shown that, if the total number of these sinks is <span>(k)</span>, then their nonwandering set consists of an even number of points which is at least <span>(2k)</span>. We have found necessary and sufficient conditions for the realizability of a set of sink periods in the minimal nonwandering set. We claim that such diffeomorphisms exist only on the 3-sphere and establish for them a sufficient condition for the existence of heteroclinic points. In addition, we prove that the Morse – Smale 3-diffeomorphism with an arbitrary set of sink periods can be implemented in the nonwandering set consisting of <span>(2k+2)</span> points. We claim that any such a diffeomorphism is supported by a lens space or the skew product <span>(mathbb{S}^{2}tilde{times}mathbb{S}^{1})</span>.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 2","pages":"226 - 253"},"PeriodicalIF":0.8,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793156","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
Affine Generalizations of the Nonholonomic Problem of a Convex Body Rolling without Slipping on the Plane 平面上无滑动滚动凸体非完整问题的仿射推广
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-03-21 DOI: 10.1134/S1560354725510021
Mariana Costa-Villegas, Luis C. García-Naranjo
{"title":"Affine Generalizations of the Nonholonomic Problem of a Convex Body Rolling without Slipping on the Plane","authors":"Mariana Costa-Villegas,&nbsp;Luis C. García-Naranjo","doi":"10.1134/S1560354725510021","DOIUrl":"10.1134/S1560354725510021","url":null,"abstract":"<div><p>We introduce a class of examples which provide an affine generalization of the nonholonomic problem of a convex body that rolls without slipping on the plane. These examples are constructed by taking as given two vector fields, one on the surface of the body and another on the plane, which specify the velocity of the contact point. We investigate dynamical aspects of the system such as existence of first integrals, smooth invariant measure, integrability\u0000and chaotic behavior, giving special attention to special shapes of the convex body and specific choices of the vector fields for which the affine nonholonomic constraints may be physically realized.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 3","pages":"354 - 381"},"PeriodicalIF":0.8,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168001","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
Parametrised KAM Theory, an Overview 参数化KAM理论综述
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-03-21 DOI: 10.1134/S156035472551001X
Henk W. Broer, Heinz Hanßmann, Florian Wagener
{"title":"Parametrised KAM Theory, an Overview","authors":"Henk W. Broer,&nbsp;Heinz Hanßmann,&nbsp;Florian Wagener","doi":"10.1134/S156035472551001X","DOIUrl":"10.1134/S156035472551001X","url":null,"abstract":"<div><p>Kolmogorov – Arnold – Moser theory started in the 1950s as the\u0000perturbation theory for persistence of multi- or\u0000quasi-periodic motions in Hamiltonian systems.\u0000Since then the theory obtained a branch where the persistent\u0000occurrence of quasi-periodicity is studied in various\u0000classes of systems, which may depend on parameters.\u0000The view changed into the direction of structural stability,\u0000concerning the occurrence of quasi-periodic tori on a set\u0000of positive Hausdorff measure in a sub-manifold of the\u0000product of phase space and parameter space.\u0000This paper contains an overview of this development with\u0000an emphasis on the world of dissipative systems, where\u0000families of quasi-periodic tori occur and bifurcate in a\u0000persistent way.\u0000The transition from orderly to chaotic dynamics here forms\u0000a leading thought.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 3","pages":"408 - 450"},"PeriodicalIF":0.8,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168002","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
Dynamical Properties of Continuous Semigroup Actions and Their Products 连续半群作用及其乘积的动力学性质
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-02-18 DOI: 10.1134/S1560354725010071
Mikhail V. Meshcheryakov, Nina I. Zhukova
{"title":"Dynamical Properties of Continuous Semigroup Actions and Their Products","authors":"Mikhail V. Meshcheryakov,&nbsp;Nina I. Zhukova","doi":"10.1134/S1560354725010071","DOIUrl":"10.1134/S1560354725010071","url":null,"abstract":"<div><p>Continuous actions of topological semigroups on products <span>(X)</span> of an arbitrary family of topological spaces <span>(X_{i})</span>, <span>(iin J,)</span> are studied. The relationship between the dynamical properties of semigroups acting on the factors <span>(X_{i})</span> and the same properties of the product of semigroups on the product <span>(X)</span> of these spaces is investigated. We consider the following dynamical properties: topological transitivity, existence of a dense orbit, density of a union of minimal sets, and density of the set of points with closed orbits. The sensitive dependence on initial conditions is investigated for countable products of metric spaces. Various examples are constructed. In particular, on an infinite-dimensional torus we have constructed a continual\u0000family of chaotic semigroup dynamical systems\u0000that are pairwise topologically not conjugate by homeomorphisms preserving the structure of the\u0000product of this torus.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 1","pages":"141 - 154"},"PeriodicalIF":0.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145122056","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
In Honor of the 90th Anniversary of Leonid Pavlovich Shilnikov (1934–2011) 纪念列昂尼德·帕夫洛维奇·希尔尼科夫90周年（1934-2011）
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-02-18 DOI: 10.1134/S1560354725010010
Sergey Gonchenko, Mikhail Malkin, Dmitry Turaev
{"title":"In Honor of the 90th Anniversary of Leonid Pavlovich Shilnikov (1934–2011)","authors":"Sergey Gonchenko,&nbsp;Mikhail Malkin,&nbsp;Dmitry Turaev","doi":"10.1134/S1560354725010010","DOIUrl":"10.1134/S1560354725010010","url":null,"abstract":"","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 1","pages":"1 - 8"},"PeriodicalIF":0.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145122059","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 Smoothness of Invariant Foliations Near a Homoclinic Bifurcation Creating Lorenz-Like Attractors 关于产生类洛伦兹吸引子的同斜分岔附近不变叶的光滑性
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-02-18 DOI: 10.1134/S1560354725010034
Mikhail I. Malkin, Klim A. Safonov
{"title":"On Smoothness of Invariant Foliations Near a Homoclinic Bifurcation Creating Lorenz-Like Attractors","authors":"Mikhail I. Malkin,&nbsp;Klim A. Safonov","doi":"10.1134/S1560354725010034","DOIUrl":"10.1134/S1560354725010034","url":null,"abstract":"<div><p>This paper deals with the problem of smoothness of the stable invariant foliation for a homoclinic bifurcation with a neutral saddle in symmetric systems of differential equations. We give an\u0000improved sufficient condition for the existence of an invariant smooth foliation on a cross-section transversal to the stable manifold of the saddle. It is shown that the smoothness of the invariant foliation depends on the gap between the leading stable eigenvalue of the saddle and other stable eigenvalues. We also obtain an equation to describe the one-dimensional factor map, and we study the renormalization properties of this map. The improved information on the smoothness of the foliation and the factor map allows one to extend Shilnikov’s results on the birth of Lorenz attractors under the bifurcation considered.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 1","pages":"26 - 44"},"PeriodicalIF":0.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145122074","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
Chain-Recurrent (C^{0})- (Omega)-Blowup in (C^{1})-Smooth Simplest Skew Products on Multidimensional Cells 链-循环(C^{0}) - (Omega) - (C^{1})中的放大-多维单元上的光滑最简单的倾斜产品
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-02-18 DOI: 10.1134/S156035472501006X
Lyudmila S. Efremova, Dmitry A. Novozhilov
{"title":"Chain-Recurrent (C^{0})- (Omega)-Blowup in (C^{1})-Smooth Simplest Skew Products on Multidimensional Cells","authors":"Lyudmila S. Efremova,&nbsp;Dmitry A. Novozhilov","doi":"10.1134/S156035472501006X","DOIUrl":"10.1134/S156035472501006X","url":null,"abstract":"<div><p>In this paper we prove criteria of a <span>(C^{0})</span>- <span>(Omega)</span>-blowup in <span>(C^{1})</span>-smooth skew products with a\u0000closed set of periodic points on multidimensional cells and give examples of maps that admit such a <span>(Omega)</span>-blowup.\u0000Our method is based on the study of the properties of the set of chain-recurrent points. We also\u0000prove that the set of weakly nonwandering points of maps under consideration coincides with\u0000the chain-recurrent set, investigate the approximation (in the <span>(C^{0})</span>-norm) and entropy properties\u0000of <span>(C^{1})</span>-smooth skew products with a closed set of periodic points.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 1","pages":"120 - 140"},"PeriodicalIF":0.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145122055","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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