Regular and Chaotic Dynamics最新文献_第3页

Maximal Tori in Infinite-Dimensional Hamiltonian Systems: a Renormalisation Group Approach 无穷维哈密顿系统中的最大环：重正化群方法

IF 0.8 4区数学

Regular and Chaotic Dynamics Pub Date : 2024-06-21 DOI: 10.1134/S1560354724540025

Livia Corsi, Guido Gentile, Michela Procesi

引用次数: 0

Geodesics with Unbounded Speed on Fluctuating Surfaces 波动曲面上速度无界的测地线

IF 0.8 4区数学

Regular and Chaotic Dynamics Pub Date : 2024-05-29 DOI: 10.1134/S1560354724030018

Andrew Clarke

{"title":"Geodesics with Unbounded Speed on Fluctuating Surfaces","authors":"Andrew Clarke","doi":"10.1134/S1560354724030018","DOIUrl":"10.1134/S1560354724030018","url":null,"abstract":"<div>We construct (C^{infty}) time-periodic fluctuating surfaces in (mathbb{R}^{3}) such that the corresponding non-autonomous geodesic flow has orbits along which the energy, and thus the speed goes to infinity. We begin with a static surface (M) in (mathbb{R}^{3}) on which the geodesic flow (with respect to the induced metric from (mathbb{R}^{3})) has a hyperbolic periodic orbit with a transverse homoclinic orbit. Taking this hyperbolic periodic orbit in an interval of energy levels gives us a normally hyperbolic invariant manifold (Lambda), the stable and unstable manifolds of which have a transverse homoclinic intersection. The surface (M) is embedded into (mathbb{R}^{3}) via a near-identity time-periodic embedding (G:Mtomathbb{R}^{3}). Then the pullback under (G) of the induced metric on (G(M)) is a time-periodic metric on (M), and the corresponding geodesic flow has a normally hyperbolic invariant manifold close to (Lambda), with stable and unstable manifolds intersecting transversely along a homoclinic channel. Perturbative techniques are used to calculate the scattering map and construct pseudo-orbits that move up along the cylinder. The energy tends to infinity along such pseudo-orbits. Finally, existing shadowing methods are applied to establish the existence of actual orbits of the non-autonomous geodesic flow shadowing these pseudo-orbits. In the same way we prove the existence of oscillatory trajectories, along which the limit inferior of the energy is finite, but the limit superior is infinite.</div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 3","pages":"435 - 450"},"PeriodicalIF":0.8,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141197649","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

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

{"title":"Numerical Evidence of Hyperbolic Dynamics and Coding of Solutions for Duffing-Type Equations with Periodic Coefficients","authors":"Mikhail E. Lebedev, Georgy L. Alfimov","doi":"10.1134/S156035472451004X","DOIUrl":"10.1134/S156035472451004X","url":null,"abstract":"<div>In this paper, we consider the equation (u_{xx}+Q(x)u+P(x)u^{3}=0) where (Q(x)) and (P(x)) are periodic\u0000functions. It is known that, if (P(x)) changes sign, a “great part” of the solutions for this\u0000equation are singular, i. e., they tend to infinity at a finite point of the real axis. Our aim is to describe as completely as possible solutions, which are regular (i. e., not singular) on (mathbb{R}). For this purpose we consider the Poincaré map (mathcal{P}) (i. e., the map-over-period) for this equation and analyse the areas of the plane ((u,u_{x})) where (mathcal{P}) and (mathcal{P}^{-1}) are defined. We give sufficient conditions for hyperbolic dynamics generated by (mathcal{P}) in these areas and show that the regular solutions correspond to a Cantor set situated in these areas. We also present a numerical algorithm for verifying these sufficient conditions at the level of “numerical evidence”. This allows us to describe regular solutions of this equation, completely or within some class, by means of symbolic dynamics. We show that regular solutions can be coded by bi-infinite sequences of symbols of some alphabet, completely or within some class. Examples of the application of this technique are given.</div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 3","pages":"451 - 473"},"PeriodicalIF":0.8,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140628477","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

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