Regular and Chaotic Dynamics最新文献_第4页

Nonlinear Dynamics of a Roller Bicycle 滚轴自行车的非线性动力学

IF 0.8 4区数学

Regular and Chaotic Dynamics Pub Date : 2024-05-06 DOI: 10.1134/S1560354724530017

Ivan A. Bizyaev, Ivan S. Mamaev

引用次数: 0

(C^{1})-Smooth (Omega)-Stable Skew Products and Completely Geometrically Integrable Self-Maps of 3D-Tori, I: (Omega)-Stability $$C^{1}$ -Smooth $$Omega$$ -Stable Skew Products and Completely Geometrically Integrable Self-Maps of 3D-Tori, I：$$Omega$$ - 稳定性

IF 0.8 4区数学

Regular and Chaotic Dynamics Pub Date : 2024-05-06 DOI: 10.1134/S1560354724520010

Lyudmila S. Efremova

引用次数: 0

Solvable Algebras and Integrable Systems 可解代数和积分系统

IF 0.8 4区数学

Regular and Chaotic Dynamics Pub Date : 2024-05-06 DOI: 10.1134/S1560354724520022

Valery V. Kozlov

引用次数: 0

Genericity of Homeomorphisms with Full Mean Hausdorff Dimension 全均值豪斯多夫维度同构的一般性

IF 0.8 4区数学

Regular and Chaotic Dynamics Pub Date : 2024-04-18 DOI: 10.1134/S1560354724510014

Jeovanny Muentes Acevedo

{"title":"Genericity of Homeomorphisms with Full Mean Hausdorff Dimension","authors":"Jeovanny Muentes Acevedo","doi":"10.1134/S1560354724510014","DOIUrl":"10.1134/S1560354724510014","url":null,"abstract":"<div>It is well known that the presence of horseshoes leads to positive entropy. If our goal is to construct a continuous map with infinite entropy, we can consider an infinite sequence of horseshoes, ensuring an unbounded number of legs.Estimating the exact values of both the metric mean dimension and mean Hausdorff dimension for a homeomorphism is a challenging task. We need to establish a precise relationship between the sizes of the horseshoes and the number of appropriated legs to control both quantities.Let (N) be an (n)-dimensional compact Riemannian manifold, where (ngeqslant 2), and (alphain[0,n]). In this paper, we construct a homeomorphism (phi:Nrightarrow N) with mean Hausdorff dimension equal to (alpha). Furthermore, we prove that the set of homeomorphisms on (N) with both lower and upper mean Hausdorff dimensions equal to (alpha) is dense in (text{Hom}(N)). Additionally, we establish that the set of homeomorphisms with upper mean Hausdorff dimension equal to (n) contains a residual subset of (text{Hom}(N).)</div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 3","pages":"474 - 490"},"PeriodicalIF":0.8,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140629052","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

Integrable Mechanical Billiards in Higher-Dimensional Space Forms 高维空间形式中的可积分机械台球

IF 0.8 4区数学

Regular and Chaotic Dynamics Pub Date : 2024-04-18 DOI: 10.1134/S1560354724510038

Airi Takeuchi, Lei Zhao

引用次数: 0

Numerical Evidence of Hyperbolic Dynamics and Coding of Solutions for Duffing-Type Equations with Periodic Coefficients 双曲动力学的数值证据和具有周期系数的达芬方程解的编码

IF 0.8 4区数学

Regular and Chaotic Dynamics Pub Date : 2024-04-18 DOI: 10.1134/S156035472451004X

Mikhail E. Lebedev, Georgy L. Alfimov

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引用次数: 0

Biasymptotically Quasi-Periodic Solutions for Time-Dependent Hamiltonians 随时间变化的哈密尔顿的近似准周期解法

IF 0.8 4区数学

Regular and Chaotic Dynamics Pub Date : 2024-04-18 DOI: 10.1134/S1560354724510026

Donato Scarcella

引用次数: 0

Extremal Black Holes as Relativistic Systems with Kepler Dynamics 作为相对论系统的极端黑洞与开普勒动力学

IF 0.8 4区数学

Regular and Chaotic Dynamics Pub Date : 2024-04-08 DOI: 10.1134/S1560354724020035

Dijs de Neeling, Diederik Roest, Marcello Seri, Holger Waalkens

{"title":"Extremal Black Holes as Relativistic Systems with Kepler Dynamics","authors":"Dijs de Neeling, Diederik Roest, Marcello Seri, Holger Waalkens","doi":"10.1134/S1560354724020035","DOIUrl":"10.1134/S1560354724020035","url":null,"abstract":"<div>The recent detection of gravitational waves emanating from inspiralling black hole binaries has triggered a renewed interest in the dynamics of relativistic two-body systems. The conservative part of the latter are given by Hamiltonian systems obtained from so-called post-Newtonian expansions of the general relativistic description of black hole binaries. In this paper we study the general question of whether there exist relativistic binaries that display Kepler-like dynamics with elliptical orbits. We show that an orbital equivalence to the Kepler problem indeed exists for relativistic systems with a Hamiltonian of a Kepler-like form. This form is realised by extremal black holes with electric charge and scalar hair to at least first order in the post-Newtonian expansion for arbitrary mass ratios and to all orders in the post-Newtonian expansion in the test-mass limit of the binary. Moreover, to fifth post-Newtonian order, we show that Hamiltonians of the Kepler-like form can be related explicitly through a canonical transformation and time reparametrisation to the Kepler problem, and that all Hamiltonians conserving a Laplace – Runge – Lenz-like vector are related in this way to Kepler.</div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 2","pages":"344 - 368"},"PeriodicalIF":0.8,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140579014","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 Interplay Between Vortices and Harmonic Flows: Hodge Decomposition of Euler’s Equations in 2d 论涡流与谐波流的相互作用：二维欧拉方程的霍奇分解

IF 0.8 4区数学

Regular and Chaotic Dynamics Pub Date : 2024-04-08 DOI: 10.1134/S1560354724020011

Clodoaldo Grotta-Ragazzo, Björn Gustafsson, Jair Koiller

{"title":"On the Interplay Between Vortices and Harmonic Flows: Hodge Decomposition of Euler’s Equations in 2d","authors":"Clodoaldo Grotta-Ragazzo, Björn Gustafsson, Jair Koiller","doi":"10.1134/S1560354724020011","DOIUrl":"10.1134/S1560354724020011","url":null,"abstract":"<div>Let (Sigma) be a compact manifold without boundary whose first homology is nontrivial. The Hodge decomposition of the incompressible Euler equation in terms of 1-forms yields a coupled PDE-ODE system. The (L^{2})-orthogonal components are a “pure” vorticity flow and a potential flow (harmonic, with the dimension of the homology). In this paper we focus on (N) point vortices on a compact Riemann surface without boundary of genus (g), with a metric chosen in the conformal class. The phase space has finite dimension (2N+2g). We compute a surface of section for the motion of a single vortex ((N=1)) on a torus ((g=1)) with a nonflat metric that shows typical features of nonintegrable 2 degrees of freedom Hamiltonians. In contradistinction, for flat tori the harmonic part is constant. Next, we turn to hyperbolic surfaces ((ggeqslant 2)) having constant curvature (-1), with discrete symmetries. Fixed points of involutions yield vortex crystals in the Poincaré disk. Finally, we consider multiply connected planar domains. The image method due to Green and Thomson is\u0000viewed in the Schottky double. The Kirchhoff – Routh Hamiltonian\u0000given in C. C. Lin’s celebrated theorem is recovered by\u0000Marsden – Weinstein reduction from (2N+2g) to (2N).\u0000The relation between the electrostatic Green function and the\u0000hydrodynamic Green function is clarified.\u0000A number of questions are suggested.</div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 2","pages":"241 - 303"},"PeriodicalIF":0.8,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140579141","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 Eisenhart’s Type Theorem for Sub-Riemannian Metrics on Step (2) Distributions with (mathrm{ad})-Surjective Tanaka Symbols 关于带有$$mathrm{ad}$$-Surjective Tanaka符号的阶$$2$分布上子黎曼度量的艾森哈特类型定理

IF 0.8 4区数学

Regular and Chaotic Dynamics Pub Date : 2024-04-08 DOI: 10.1134/S1560354724020023

Zaifeng Lin, Igor Zelenko

引用次数: 0