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On Homeomorphisms of Three-Dimensional Manifolds with Pseudo-Anosov Attractors and Repellers 论具有伪阿诺索夫吸引子和排斥子的三维流形的同构性
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S1560354724010106
Vyacheslav Z. Grines, Olga V. Pochinka, Ekaterina E. Chilina
{"title":"On Homeomorphisms of Three-Dimensional Manifolds with Pseudo-Anosov Attractors and Repellers","authors":"Vyacheslav Z. Grines,&nbsp;Olga V. Pochinka,&nbsp;Ekaterina E. Chilina","doi":"10.1134/S1560354724010106","DOIUrl":"10.1134/S1560354724010106","url":null,"abstract":"<div><p>The present paper is devoted to a study of orientation-preserving homeomorphisms on three-dimensional manifolds with a non-wandering set consisting of a finite number of surface attractors and repellers. The main results of the paper relate to a class of homeomorphisms for which the restriction of the map to a connected component of the non-wandering set is topologically conjugate to an orientation-preserving pseudo-Anosov homeomorphism. The ambient <span>(Omega)</span>-conjugacy of a homeomorphism from the class with a locally direct product of a pseudo-Anosov homeomorphism and a rough transformation of the circle is proved. In addition, we prove that the centralizer of a pseudo-Anosov homeomorphisms consists of only pseudo-Anosov and periodic maps.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"156 - 173"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099200","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 Regularity of Invariant Foliations 论不变叶形的规律性
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S1560354724010027
Dmitry Turaev
{"title":"On the Regularity of Invariant Foliations","authors":"Dmitry Turaev","doi":"10.1134/S1560354724010027","DOIUrl":"10.1134/S1560354724010027","url":null,"abstract":"<div><p>We show that the stable invariant foliation of codimension 1 near a zero-dimensional hyperbolic set of a <span>(C^{beta})</span> map with <span>(beta&gt;1)</span> is <span>(C^{1+varepsilon})</span> with some <span>(varepsilon&gt;0)</span>. The result is applied to the restriction of higher regularity\u0000maps to normally hyperbolic manifolds. An application to the theory of the Newhouse phenomenon is discussed.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"6 - 24"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140098869","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
Asymptotics of Self-Oscillations in Chains of Systems of Nonlinear Equations 非线性方程系统链中自振荡的渐近性
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S1560354724010143
Sergey A. Kashchenko
{"title":"Asymptotics of Self-Oscillations in Chains of Systems of Nonlinear Equations","authors":"Sergey A. Kashchenko","doi":"10.1134/S1560354724010143","DOIUrl":"10.1134/S1560354724010143","url":null,"abstract":"<div><p>We study the local dynamics of chains of coupled nonlinear systems of second-order ordinary differential equations of diffusion-difference type. The main assumption is that the number of elements of chains is large enough. This condition allows us to pass to the problem with a continuous spatial variable.\u0000Critical cases have been considered while studying the stability of the equilibrum state.\u0000It is shown that all these cases have infinite dimension. The research technique is based on the development and application of special methods for construction of normal forms.\u0000Among the main results of the paper, we include the creation of new nonlinear boundary value problems of parabolic type, whose nonlocal dynamics describes the local behavior of solutions of the original system.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"218 - 240"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099152","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
Quasi-Periodicity at Transition from Spiking to Bursting in the Pernarowski Model of Pancreatic Beta Cells 胰腺β细胞的 Pernarowski 模型中从尖峰到爆发的准周期性转变
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S1560354724010076
Haniyeh Fallah, Andrey L. Shilnikov
{"title":"Quasi-Periodicity at Transition from Spiking to Bursting in the Pernarowski Model of Pancreatic Beta Cells","authors":"Haniyeh Fallah,&nbsp;Andrey L. Shilnikov","doi":"10.1134/S1560354724010076","DOIUrl":"10.1134/S1560354724010076","url":null,"abstract":"<div><p>This paper studies quasi-periodicity phenomena appearing at the transition from spiking to bursting activities in the Pernarowski model of pancreatic beta cells. Continuing the parameter, we show that the torus bifurcation is responsible for the transition between spiking and bursting. Our investigation involves different torus bifurcations, such as supercritical torus bifurcation, saddle torus canard, resonant torus, self-similar torus fractals, and torus destruction. These bifurcations give rise to complex or multistable dynamics. Despite being a dissipative system, the model still exhibits KAM tori, as we have illustrated. We provide two scenarios for the onset of resonant tori using the Poincaré return map, where global bifurcations happen because of the saddle-node or inverse period-doubling bifurcations. The blue-sky catastrophe takes place at the transition route from bursting to spiking.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"100 - 119"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099144","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
Quasi-Periodic Parametric Perturbations of Two-Dimensional Hamiltonian Systems with Nonmonotonic Rotation 具有非单调旋转的二维哈密顿系统的准周期参数扰动
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S1560354724010052
Kirill E. Morozov, Albert D. Morozov
{"title":"Quasi-Periodic Parametric Perturbations of Two-Dimensional Hamiltonian Systems with Nonmonotonic Rotation","authors":"Kirill E. Morozov,&nbsp;Albert D. Morozov","doi":"10.1134/S1560354724010052","DOIUrl":"10.1134/S1560354724010052","url":null,"abstract":"<div><p>We study nonconservative quasi-periodic (with <span>(m)</span> frequencies) perturbations of two-dimensional Hamiltonian systems with nonmonotonic rotation. It is assumed that the perturbation contains the so-called <i>parametric</i> terms. The behavior of solutions in the vicinity of degenerate resonances is described. Conditions for the existence of resonance <span>((m+1))</span>-dimensional invariant tori for which there are no generating ones in the unperturbed system are found. The class of perturbations for which such tori can exist is indicated. The results are applied to the asymmetric Duffing equation under a parametric quasi-periodic perturbation.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"65 - 77"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099143","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
Universal Transient Dynamics in Oscillatory Network Models of Epileptic Seizures 癫痫发作振荡网络模型中的通用瞬态动力学
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S156035472401012X
Anton A. Kapustnikov, Marina V. Sysoeva, Ilya V. Sysoev
{"title":"Universal Transient Dynamics in Oscillatory Network Models of Epileptic Seizures","authors":"Anton A. Kapustnikov,&nbsp;Marina V. Sysoeva,&nbsp;Ilya V. Sysoev","doi":"10.1134/S156035472401012X","DOIUrl":"10.1134/S156035472401012X","url":null,"abstract":"<div><p>Discharges of different epilepsies are characterized by different signal shape and duration.\u0000The authors adhere to the hypothesis that spike-wave discharges are long transient processes rather than attractors. This helps to explain some experimentally observed properties of discharges, including the\u0000absence of a special termination mechanism and quasi-regularity.\u0000Analytical approaches mostly cannot be applied to studying transient dynamics in large networks. Therefore, to test the observed phenomena for universality one has to show that the same results can be achieved using different model types for nodes and different connectivity terms. Here, we study a class of simple network\u0000models of a thalamocortical system and show that for the same connectivity matrices long, but finite in time quasi-regular processes mimicking epileptic spike-wave discharges can be found using nodes described by three neuron models: FitzHugh – Nagumo, Morris – Lecar and Hodgkin – Huxley. This result\u0000takes place both for linear and nonlinear sigmoid coupling.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"190 - 204"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099150","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
Classification of Axiom A Diffeomorphisms with Orientable Codimension One Expanding Attractors and Contracting Repellers 具有可定向一维扩展吸引子和收缩排斥子的公理 A 衍变的分类
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S156035472401009X
Vyacheslav Z. Grines, Vladislav S. Medvedev, Evgeny V. Zhuzhoma
{"title":"Classification of Axiom A Diffeomorphisms with Orientable Codimension One Expanding Attractors and Contracting Repellers","authors":"Vyacheslav Z. Grines,&nbsp;Vladislav S. Medvedev,&nbsp;Evgeny V. Zhuzhoma","doi":"10.1134/S156035472401009X","DOIUrl":"10.1134/S156035472401009X","url":null,"abstract":"<div><p>Let <span>(mathbb{G}_{k}^{cod1}(M^{n}))</span>, <span>(kgeqslant 1)</span>, be the set of axiom A diffeomorphisms such that\u0000the nonwandering set of any <span>(finmathbb{G}_{k}^{cod1}(M^{n}))</span> consists of <span>(k)</span> orientable connected codimension one expanding attractors and contracting repellers where <span>(M^{n})</span> is a closed orientable <span>(n)</span>-manifold, <span>(ngeqslant 3)</span>. We classify the diffeomorphisms from <span>(mathbb{G}_{k}^{cod1}(M^{n}))</span> up to the global conjugacy on nonwandering sets. In addition, we show that any <span>(finmathbb{G}_{k}^{cod1}(M^{n}))</span> is <span>(Omega)</span>-stable and is not structurally stable. One describes the topological structure of a supporting manifold <span>(M^{n})</span>.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"143 - 155"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099154","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
Sensitivity and Chaoticity of Some Classes of Semigroup Actions 几类半群作用的敏感性和混沌性
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI: 10.1134/S1560354724010118
Nina I. Zhukova
{"title":"Sensitivity and Chaoticity of Some Classes of Semigroup Actions","authors":"Nina I. Zhukova","doi":"10.1134/S1560354724010118","DOIUrl":"10.1134/S1560354724010118","url":null,"abstract":"<div><p>The focus of the work is the investigation of chaos and closely related dynamic properties of continuous actions of almost open\u0000semigroups and <span>(C)</span>-semigroups. The class of dynamical systems <span>((S,X))</span> defined by such semigroups <span>(S)</span> is denoted by <span>(mathfrak{A})</span>.\u0000These semigroups contain, in particular, cascades, semiflows and groups of homeomorphisms. We extend the Devaney definition of chaos to general dynamical systems. For <span>((S,X)inmathfrak{A})</span> on locally compact metric spaces <span>(X)</span> with a countable base we\u0000prove that topological transitivity and density of the set formed by points having closed orbits imply the sensitivity to initial conditions. We assume neither the compactness of metric space nor the compactness of the above-mentioned closed orbits.\u0000In the case when the set of points having compact orbits is dense, our proof proceeds without the assumption of local compactness of the phase space <span>(X)</span>. This statement generalizes the well-known result of J. Banks et al. on Devaney’s definition\u0000of chaos for cascades.The interrelation of sensitivity, transitivity and the property of minimal sets of semigroups is investigated. Various examples are given.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"174 - 189"},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099201","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
Slow-Fast Systems with an Equilibrium Near the Folded Slow Manifold 在折叠慢速歧面附近达到平衡的慢-快系统
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-12-19 DOI: 10.1134/S156035472354002X
Natalia G. Gelfreikh, Alexey V. Ivanov
{"title":"Slow-Fast Systems with an Equilibrium Near the Folded Slow Manifold","authors":"Natalia G. Gelfreikh,&nbsp;Alexey V. Ivanov","doi":"10.1134/S156035472354002X","DOIUrl":"10.1134/S156035472354002X","url":null,"abstract":"<div><p>We study a slow-fast system with two slow and one fast variables.\u0000We assume that the slow manifold of the system possesses a fold and there is an equilibrium of the system in a small neighborhood of the fold. We derive a normal form for the system\u0000in a neighborhood of the pair “equilibrium-fold”\u0000and study the dynamics of the normal form. In particular, as the ratio of two time scales tends to zero we obtain an asymptotic formula for the Poincaré map\u0000and calculate the parameter values for the first period-doubling bifurcation. The theory is applied to a generalization of the FitzHugh – Nagumo system.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 2","pages":"376 - 403"},"PeriodicalIF":0.8,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138743675","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
Hyperbolic Attractors Which are Anosov Tori 属于阿诺索夫环的双曲吸引子
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-12-19 DOI: 10.1134/S1560354723540018
Marina K. Barinova, Vyacheslav Z. Grines, Olga V. Pochinka, Evgeny V. Zhuzhoma
{"title":"Hyperbolic Attractors Which are Anosov Tori","authors":"Marina K. Barinova,&nbsp;Vyacheslav Z. Grines,&nbsp;Olga V. Pochinka,&nbsp;Evgeny V. Zhuzhoma","doi":"10.1134/S1560354723540018","DOIUrl":"10.1134/S1560354723540018","url":null,"abstract":"<div><p>We consider a topologically mixing hyperbolic attractor <span>(Lambdasubset M^{n})</span> for a diffeomorphism <span>(f:M^{n}to M^{n})</span> of a compact orientable <span>(n)</span>-manifold <span>(M^{n})</span>, <span>(n&gt;3)</span>. Such an attractor <span>(Lambda)</span> is called an Anosov torus provided the restriction <span>(f|_{Lambda})</span> is conjugate to Anosov algebraic automorphism of <span>(k)</span>-dimensional torus <span>(mathbb{T}^{k})</span>.\u0000We prove that <span>(Lambda)</span> is an Anosov torus for two cases:\u00001) <span>(dim{Lambda}=n-1)</span>, <span>(dim{W^{u}_{x}}=1)</span>, <span>(xinLambda)</span>;\u00002) <span>(dimLambda=k,dim W^{u}_{x}=k-1,xinLambda)</span>, and <span>(Lambda)</span> belongs to an <span>(f)</span>-invariant closed <span>(k)</span>-manifold, <span>(2leqslant kleqslant n)</span>, topologically embedded in <span>(M^{n})</span>.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 2","pages":"369 - 375"},"PeriodicalIF":0.8,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138743744","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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