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Regular and Chaotic Dynamics最新文献

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Symplectic Classification for Universal Unfoldings of (A_{n}) Singularities in Integrable Systems 可积系统中(A_{n})奇点全称展开的辛分类
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-08-11 DOI: 10.1134/S1560354725040124
Elena A. Kudryavtseva
{"title":"Symplectic Classification for Universal Unfoldings of (A_{n}) Singularities in Integrable Systems","authors":"Elena A. Kudryavtseva","doi":"10.1134/S1560354725040124","DOIUrl":"10.1134/S1560354725040124","url":null,"abstract":"<div><p>In the present paper, we obtain real-analytic symplectic normal forms for integrable Hamiltonian\u0000systems with <span>(n)</span> degrees of freedom in small neighborhoods of singular points having the type “universal unfolding of <span>(A_{n})</span> singularity”, <span>(ngeqslant 1)</span> (local singularities), as well as in small neighborhoods of compact orbits containing such singular points (semilocal singularities).\u0000We also obtain a classification, up to real-analytic symplectic equivalence, of real-analytic Lagrangian foliations in saturated neighborhoods of such singular orbits (semiglobal classification).\u0000These corank-one singularities (local, semilocal and semiglobal ones) are structurally stable.\u0000It turns out that all integrable systems are symplectically equivalent near their singular points of this type, thus there are no local symplectic invariants.\u0000A complete semilocal (respectively, semiglobal) symplectic invariant of the singularity\u0000is given by a tuple of <span>(n-1)</span> (respectively <span>(n-1+ell)</span>) real-analytic function germs in <span>(n)</span> variables, where <span>(ell)</span> is the number of connected components of the complement of the singular orbit in the fiber.\u0000The case <span>(n=1)</span> corresponds to nondegenerate singularities (of elliptic and hyperbolic types)\u0000of one-degree-of-freedom Hamiltonians; their symplectic classifications were known.\u0000The case <span>(n=2)</span> corresponds to parabolic points, parabolic orbits and cuspidal tori.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 Editors:","pages":"639 - 665"},"PeriodicalIF":0.8,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121786","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
Valery V. Kozlov On the Occasion of his 75th Birthday 瓦列里·v·科兹洛夫在他75岁生日之际
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-08-11 DOI: 10.1134/S156035472504001X
{"title":"Valery V. Kozlov On the Occasion of his 75th Birthday","authors":"","doi":"10.1134/S156035472504001X","DOIUrl":"10.1134/S156035472504001X","url":null,"abstract":"","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 Editors:","pages":"463 - 463"},"PeriodicalIF":0.8,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121788","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
The Ozawa Solution to the Davey – Stewartson II Equations and Surface Theory Davey - Stewartson II方程的Ozawa解和曲面理论
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-08-11 DOI: 10.1134/S1560354725040100
Yi C. Huang, Iskander A. Taimanov
{"title":"The Ozawa Solution to the Davey – Stewartson II Equations and Surface Theory","authors":"Yi C. Huang,&nbsp;Iskander A. Taimanov","doi":"10.1134/S1560354725040100","DOIUrl":"10.1134/S1560354725040100","url":null,"abstract":"<div><p>We describe the Ozawa solution to the Davey – Stewartson II equation from the point of view of surface theory by presenting a soliton deformation of surfaces which is ruled by the Ozawa solution. The Ozawa solution blows up at a certain moment and we describe explicitly the corresponding singularity of the deformed surface.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 Editors:","pages":"612 - 617"},"PeriodicalIF":0.8,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121372","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
Nonsingular Flows with a Twisted Saddle Orbit on Orientable 3-Manifolds 可定向3-流形上具有扭曲鞍轨道的非奇异流
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-08-11 DOI: 10.1134/S1560354725040161
Olga V. Pochinka, Danila D. Shubin
{"title":"Nonsingular Flows with a Twisted Saddle Orbit on Orientable 3-Manifolds","authors":"Olga V. Pochinka,&nbsp;Danila D. Shubin","doi":"10.1134/S1560354725040161","DOIUrl":"10.1134/S1560354725040161","url":null,"abstract":"<div><p>In this paper we consider nonsingular Morse – Smale flows on closed orientable 3-manifolds, under the assumption that among the periodic orbits of the flow there is only one saddle orbit and it is twisted. It is found that any manifold admitting such flows is either a lens space, or a connected sum of a lens space with a projective space, or Seifert manifolds with base sphere and three special layers. A complete topological classification of the described flows is obtained and the number of their equivalence classes on each admissible manifold is calculated.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 Editors:","pages":"711 - 731"},"PeriodicalIF":0.8,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121787","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
Realization of (A)-Diffeomorphisms of Surfaces with Connected One-Dimensional Basic Sets 一维基本集连通曲面的(A) -微分同胚的实现
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-08-04 DOI: 10.1134/S156035472552003X
Vyacheslav Grines, Dmitrii Mints, Alexey Zhirov
{"title":"Realization of (A)-Diffeomorphisms of Surfaces with Connected One-Dimensional Basic Sets","authors":"Vyacheslav Grines,&nbsp;Dmitrii Mints,&nbsp;Alexey Zhirov","doi":"10.1134/S156035472552003X","DOIUrl":"10.1134/S156035472552003X","url":null,"abstract":"<div><p>This paper is a continuation of our previous work where we investigated\u0000the class <span>(mathbb{G}(M^{2}))</span> of <span>(A)</span>-diffeomorphisms of closed orientable connected surfaces such\u0000that their nonwandering sets consist of one-dimensional basic sets (attractors and repellers).\u0000In that work, we showed that the dynamical properties of each diffeomorphism from a given\u0000class define a collection consisting of nonempty multisets of natural numbers (each such\u0000collection contains at least two multisets). These multisets are topological invariants of\u0000the diffeomorphism and uniquely determine the topology of the ambient surface. In this paper,\u0000we solve the problem of realization of diffeomorphisms from the class <span>(mathbb{G}(M^{2}))</span> with\u0000respect to a given collection of multisets of natural numbers. We describe all possible\u0000collections of multisets from which one can construct a diffeomorphism from the class\u0000<span>(mathbb{G}(M^{2}))</span>, presenting a step-by-step algorithm of construction.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 3","pages":"391 - 406"},"PeriodicalIF":0.8,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148060966","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
The Birkhoff Normal Form through the Lens of Representation Theory 从表征理论的视角看Birkhoff范式
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-08-04 DOI: 10.1134/S1560354725520016
Richard Montgomery
{"title":"The Birkhoff Normal Form through the Lens of Representation Theory","authors":"Richard Montgomery","doi":"10.1134/S1560354725520016","DOIUrl":"10.1134/S1560354725520016","url":null,"abstract":"<div><p>We derive the simplest version of the finite-order Birkhoff normal forms [BNFs], that for area-preserving maps of the plane,\u0000using the finite-dimensional representation theory for the group of linear area-preserving maps of that plane and of its circle subgroup. We describe our motivation: the utility of understanding the 3rd-order BNF to obtain KAM stability for non-trivial\u0000periodic orbits which arise in celestial mechanics.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 Editors:","pages":"952 - 961"},"PeriodicalIF":0.8,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145646328","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
Computing the Dynamical Core of Horseshoe Homoclinic Orbits 马蹄形同斜轨道动力核的计算
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-08-04 DOI: 10.1134/S1560354725520028
Valentín Mendoza
{"title":"Computing the Dynamical Core of Horseshoe Homoclinic Orbits","authors":"Valentín Mendoza","doi":"10.1134/S1560354725520028","DOIUrl":"10.1134/S1560354725520028","url":null,"abstract":"<div><p>The dynamics that necessarily coexists with a homoclinic orbit is captured by its dynamical core.\u0000In this work we characterize the dynamical core of a broad class of homoclinic orbits in the Smale horseshoe,\u0000specifically those with decorations of three types: maximal, P-lists and star decorations.\u0000For each of these families, we construct an explicit pruning region whose survival set — consisting of all symbolic sequences whose orbits avoid the region under the shift — coincides with the dynamical core.\u0000This provides a unified symbolic description of the forced dynamics and establishes a framework\u0000for computing dynamical invariants such as topological entropy.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"31 3","pages":"370 - 390"},"PeriodicalIF":0.8,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148060965","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
Closed Servoconstraints in Periodic Motion Planning for Underactuated Mechanical Systems 欠驱动机械系统周期运动规划中的封闭伺服约束
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-06-04 DOI: 10.1134/S1560354725030013
Maksim O. Surov, Maksim Yu. Grigorov
{"title":"Closed Servoconstraints in Periodic Motion Planning for Underactuated Mechanical Systems","authors":"Maksim O. Surov,&nbsp;Maksim Yu. Grigorov","doi":"10.1134/S1560354725030013","DOIUrl":"10.1134/S1560354725030013","url":null,"abstract":"<div><p>This paper is devoted to the servoconstraints approach in the problem of periodic motion planning for Euler – Lagrange systems with a single degree of underactuation.\u0000We focus on the case where the servoconstraint is not regular and thus leads to the appearance of isolated singularities in reduced dynamics. We demonstrate that, subject to supplementary conditions, the reduced dynamics possess smooth solutions that pass through the singular point and this can be utilized for finding trajectories of the original system. Building upon this outcome, we solve the problem of motion planning of the Pendubot system\u0000with an imposed eight-shaped servoconstraint. To verify the feasibility of the discovered\u0000trajectory, we present computer simulation results\u0000of the closed-loop system with feedback that enables orbital stabilization\u0000for the trajectory.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 3","pages":"451 - 462"},"PeriodicalIF":0.8,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161929","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
Scientific Heritage of L. P. Shilnikov. Part II. Homoclinic Chaos 希尔尼科夫的科学遗产。第二部分.同线性混沌
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-04-07 DOI: 10.1134/S1560354725020017
Sergey V. Gonchenko, Lev M. Lerman, Andrey L. Shilnikov, Dmitry V. Turaev
{"title":"Scientific Heritage of L. P. Shilnikov. Part II. Homoclinic Chaos","authors":"Sergey V. Gonchenko,&nbsp;Lev M. Lerman,&nbsp;Andrey L. Shilnikov,&nbsp;Dmitry V. Turaev","doi":"10.1134/S1560354725020017","DOIUrl":"10.1134/S1560354725020017","url":null,"abstract":"<div><p>We review the works initiated and developed by L. P. Shilnikov on homoclinic chaos, highlighting his fundamental contributions to Poincaré homoclinics to periodic orbits and invariant tori. Additionally, we discuss his related findings in non-autonomous and infinite-dimensional systems. This survey continues our earlier review [1], where we examined Shilnikov’s groundbreaking results on bifurcations of homoclinic orbits — his extension of the classical work by A. A. Andronov and E. A. Leontovich from planar to multidimensional autonomous systems, as well as his pioneering discoveries on saddle-focus loops and spiral chaos.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 2","pages":"155 - 173"},"PeriodicalIF":0.8,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793155","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
Scenarios for the Creation of Hyperchaotic Attractors with Three Positive Lyapunov Exponents 产生具有三个正 Lyapunov 指数的超混沌吸引子的情景
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-04-07 DOI: 10.1134/S156035472502008X
Efrosiniia Karatetskaia, Aikan Shykhmamedov, Konstantin Soldatkin, Alexey Kazakov
{"title":"Scenarios for the Creation of Hyperchaotic Attractors with Three Positive Lyapunov Exponents","authors":"Efrosiniia Karatetskaia,&nbsp;Aikan Shykhmamedov,&nbsp;Konstantin Soldatkin,&nbsp;Alexey Kazakov","doi":"10.1134/S156035472502008X","DOIUrl":"10.1134/S156035472502008X","url":null,"abstract":"<div><p>We study hyperchaotic attractors characterized by three positive Lyapunov exponents in numerical experiments. In order to possess this property, periodic orbits belonging to the attractor should have a three-dimensional unstable invariant manifold. Starting with a stable fixed point we describe several bifurcation scenarios that create such periodic orbits inside the attractor. These scenarios include cascades of alternating period-doubling and Neimark – Sacker bifurcations which, as we show, naturally appear near the cascade of codimension-2 period-doubling bifurcations, when periodic orbits along the cascade have multipliers <span>((-1,e^{iphi},e^{-iphi}))</span>. The proposed scenarios are illustrated by examples of the three-dimensional Kaneko endomorphism and a four-dimensional Hénon map.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 2","pages":"306 - 324"},"PeriodicalIF":0.8,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793152","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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