Regular and Chaotic Dynamics最新文献

On Partially Hyperbolic Diffeomorphisms and Regular Denjoy Type Homeomorphisms 部分双曲微分同态和正则Denjoy型同态

IF 1.4 4区数学

Regular and Chaotic Dynamics Pub Date : 2023-06-02 DOI: 10.1134/S1560354723030036

Vyacheslav Z. Grines, Dmitrii I. Mints

{"title":"On Partially Hyperbolic Diffeomorphisms and Regular Denjoy Type Homeomorphisms","authors":"Vyacheslav Z. Grines, Dmitrii I. Mints","doi":"10.1134/S1560354723030036","DOIUrl":"10.1134/S1560354723030036","url":null,"abstract":"<div><p>In P. D. McSwiggen’s article, it was proposed Derived from Anosov type construction which leads to a partially hyperbolic diffeomorphism of the 3-torus. The nonwandering set of this diffeomorphism contains a two-dimensional attractor which consists of one-dimensional unstable manifolds of its points. The constructed\u0000diffeomorphism admits an invariant one-dimensional orientable foliation such that it contains\u0000unstable manifolds of points of the attractor as its leaves. Moreover, this foliation has a\u0000global cross section (2-torus) and defines on it a Poincaré map which is a regular Denjoy\u0000type homeomorphism. Such homeomorphisms are the most natural generalization of Denjoy\u0000homeomorphisms of the circle and play an important role in the description of the dynamics\u0000of aforementioned partially hyperbolic diffeomorphisms. In particular, the topological\u0000conjugacy of corresponding Poincaré maps provides necessary conditions for the topological\u0000conjugacy of the restrictions of such partially hyperbolic diffeomorphisms to\u0000their two-dimensional attractors. The nonwandering set of each regular Denjoy type homeomorphism\u0000is a Sierpiński set and each such homeomorphism is, by definition, semiconjugate to the\u0000minimal translation of the 2-torus. We introduce a complete invariant of topological conjugacy\u0000for regular Denjoy type homeomorphisms that is characterized by the minimal translation,\u0000which is semiconjugation of the given regular Denjoy type homeomorphism, with a distinguished,\u0000no more than countable set of orbits.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 3","pages":"295 - 308"},"PeriodicalIF":1.4,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4090578","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

Numerical and Theoretical Studies on the Rational Standard Map at Moderate-to-Large Values of the Amplitude Parameter 幅值参数中大值的有理标准图的数值与理论研究

IF 1.4 4区数学

Regular and Chaotic Dynamics Pub Date : 2023-06-02 DOI: 10.1134/S1560354723030024

Pablo M. Cincotta, Claudia M. Giordano, Carles Simó

引用次数: 0

Parametric Resonance of a Charged Pendulum with a Suspension Point Oscillating Between Two Vertical Charged Lines 悬点在两条垂直带电线之间振荡的带电摆的参数共振

IF 1.4 4区数学

Regular and Chaotic Dynamics Pub Date : 2023-06-02 DOI: 10.1134/S156035472303005X

Adecarlos C. Carvalho, Gerson C. Araujo

引用次数: 0

Formal Stability, Stability for Most Initial Conditions and Diffusion in Analytic Systems of Differential Equations 形式稳定性，大多数初始条件的稳定性和微分方程解析系统的扩散

IF 1.4 4区数学

Regular and Chaotic Dynamics Pub Date : 2023-06-02 DOI: 10.1134/S1560354723030012

Valery V. Kozlov

引用次数: 0

A Note on the Weighted Yamabe Flow 关于加权Yamabe流的注释

IF 1.4 4区数学

Regular and Chaotic Dynamics Pub Date : 2023-06-02 DOI: 10.1134/S1560354723030048

Theodore Yu. Popelensky

引用次数: 0

Smale Regular and Chaotic A-Homeomorphisms and A-Diffeomorphisms 小正则和混沌a -同胚和a -异胚

IF 1.4 4区数学

Regular and Chaotic Dynamics Pub Date : 2023-04-07 DOI: 10.1134/S1560354723020016

Vladislav S. Medvedev, Evgeny V. Zhuzhoma

{"title":"Smale Regular and Chaotic A-Homeomorphisms and A-Diffeomorphisms","authors":"Vladislav S. Medvedev, Evgeny V. Zhuzhoma","doi":"10.1134/S1560354723020016","DOIUrl":"10.1134/S1560354723020016","url":null,"abstract":"<div><p>We introduce Smale A-homeomorphisms that include regular, semichaotic, chaotic, and\u0000superchaotic homeomorphisms of a topological <span>(n)</span>-manifold <span>(M^{n})</span>, <span>(ngeqslant 2)</span>. Smale A-homeomorphisms contain axiom A diffeomorphisms (in short, A-diffeomorphisms) provided that <span>(M^{n})</span> admits a smooth structure. Regular A-homeomorphisms contain all Morse – Smale diffeomorphisms, while semichaotic and chaotic A-homeomorphisms contain A-diffeomorphisms with trivial and nontrivial basic sets. Superchaotic A-homeomorphisms contain A-diffeomorphisms whose basic sets are nontrivial. The reason to consider Smale A-homeomorphisms instead of A-diffeomorphisms may be attributed to the fact that it is a good weakening of nonuniform hyperbolicity and pseudo-hyperbolicity, a subject which has already seen an immense number of applications.</p><p>We describe invariant sets that determine completely the dynamics of regular, semichaotic, and chaotic Smale A-homeomorphisms. This allows us to get necessary and sufficient conditions of conjugacy for these Smale A-homeomorphisms (in particular, for all Morse – Smale diffeomorphisms). We apply\u0000these necessary and sufficient conditions for structurally stable surface diffeomorphisms\u0000with an arbitrary number of expanding attractors. We also use these conditions to obtain a\u0000complete classification of Morse – Smale diffeomorphisms on projective-like manifolds.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 2","pages":"131 - 147"},"PeriodicalIF":1.4,"publicationDate":"2023-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4281926","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

Stability Analysis of Resonant Rotation of a Gyrostat in an Elliptic Orbit Under Third-and Fourth-Order Resonances 椭圆轨道陀螺三阶和四阶共振旋转稳定性分析

IF 1.4 4区数学

Regular and Chaotic Dynamics Pub Date : 2023-04-07 DOI: 10.1134/S156035472302003X

Xue Zhong, Jie Zhao, Kaiping Yu, Minqiang Xu

{"title":"Stability Analysis of Resonant Rotation of a Gyrostat in an Elliptic Orbit Under Third-and Fourth-Order Resonances","authors":"Xue Zhong, Jie Zhao, Kaiping Yu, Minqiang Xu","doi":"10.1134/S156035472302003X","DOIUrl":"10.1134/S156035472302003X","url":null,"abstract":"<div><p>This paper presents the stability of resonant rotation of a symmetric gyrostat under third- and fourth-order resonances, whose center of mass moves in an elliptic orbit in a central Newtonian gravitational field. The resonant rotation is a special planar periodic motion of the gyrostat about its center of mass, i. e., the body performs one rotation in absolute space during two orbital revolutions of its center of mass. The equations of motion of\u0000the gyrostat are derived as a periodic Hamiltonian system with three degrees of freedom and a constructive algorithm based on a symplectic map is used to calculate the coefficients of the normalized Hamiltonian. By analyzing the Floquet multipliers of the linearized equations of perturbed motion, the unstable region of the resonant rotation and the region of stability in the first-order approximation are determined in the dimensionless parameter plane. In addition, the third- and fourth-order resonances are obtained in the linear stability region and further nonlinear stability analysis is performed in the third- and fourth-order resonant cases.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 2","pages":"162 - 190"},"PeriodicalIF":1.4,"publicationDate":"2023-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4280155","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

Analyzing the Motion of a Washer on a Rod 分析一杆上的垫圈运动

IF 1.4 4区数学

Regular and Chaotic Dynamics Pub Date : 2023-04-07 DOI: 10.1134/S1560354723020065

Hiroshi Takano

{"title":"Analyzing the Motion of a Washer on a Rod","authors":"Hiroshi Takano","doi":"10.1134/S1560354723020065","DOIUrl":"10.1134/S1560354723020065","url":null,"abstract":"<div><p>This paper investigates the dynamics of a toy known as the chatter ring.\u0000Specifically, it examines the mechanism by which the small ring rotates around the large ring,\u0000the mechanism by which\u0000the force from the large ring provides torque to the small ring, and\u0000whether the motion of the small ring is the same as that of a hula hoop.\u0000The dynamics of a chatter ring has been investigated in previous work [13, 14, 15];\u0000however, a detailed analysis has not yet been performed.\u0000Thus, to understand the mechanisms described above,\u0000the equations of motion and constraint conditions\u0000are obtained, and an analysis of the motion is performed.\u0000To simplify the problem, a model consisting of\u0000a straight rod and a washer ring is analyzed under the no-slip condition.\u0000The motion of a washer has two modes: the one point of contact (1PC) mode and\u0000two points of contact (2PC) mode.\u0000The motion of the small ring of the chatter ring is similar\u0000to that of a washer in the 2PC mode,\u0000whereas the motion of a hula hoop is similar to that\u0000of a washer in the 1PC mode.\u0000The analysis indicates that the motion of a washer with two points of contact\u0000is equivalent to free fall motion. However, in practice, the velocity reaches a constant\u0000value through energy dissipation.\u0000The washer rotates around an axis that passes through the two points of contact.\u0000The components of the forces exerted by the rod at the points of contact that are normal to the plane of the washer\u0000provide rotational torque acting at the center of mass.\u0000The components of the forces parallel to the horizontal plane\u0000are centripetal forces, which\u0000induce the circular motion of the center of mass.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 2","pages":"227 - 250"},"PeriodicalIF":1.4,"publicationDate":"2023-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4280159","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

Using Couplings to Suppress Chaos and Produce a Population Stabilisation Strategy 利用耦合抑制混沌并产生种群稳定策略

IF 1.4 4区数学

Regular and Chaotic Dynamics Pub Date : 2023-04-07 DOI: 10.1134/S1560354723020041

Luís M. Lopes, Clara Grácio, Sara Fernandes, Danièle Fournier-Prunaret

引用次数: 0

Spiral-Like Extremals near a Singular Surface in a Rocket Control Problem 一类火箭控制问题奇异曲面附近的螺旋形极值

IF 1.4 4区数学

Regular and Chaotic Dynamics Pub Date : 2023-04-07 DOI: 10.1134/S1560354723020028

Mariya I. Ronzhina, Larisa A. Manita

引用次数: 1