发布求助
文献互助 智能选刊 最新文献

Regular and Chaotic Dynamics最新文献

筛选
英文 中文
Lyapunov Exponents of Linear Switched Systems 线性切换系统的Lyapunov指数
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-08-11 DOI: 10.1134/S1560354725040033
Andrei A. Agrachev, Michele Motta
{"title":"Lyapunov Exponents of Linear Switched Systems","authors":"Andrei A. Agrachev,&nbsp;Michele Motta","doi":"10.1134/S1560354725040033","DOIUrl":"10.1134/S1560354725040033","url":null,"abstract":"<div><p>We explicitly compute the maximal Lyapunov exponent for a switched system on <span>(mathrm{SL}_{2}(mathbb{R}))</span> and the corresponding switching function which realizes the maximal exponent. This computation is reduced to the characterization of optimal trajectories for an optimal control problem on the Lie group.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 Editors:","pages":"481 - 503"},"PeriodicalIF":0.8,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121373","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 Picard – Lindelöf Argument and the Banach – Caccioppoli Contraction Mapping Principle 论皮卡德- Lindelöf论证和巴拿赫-卡乔波利收缩映射原理
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-08-11 DOI: 10.1134/S1560354725040070
Alexander I. Bufetov, Ilya I. Zavolokin
{"title":"On the Picard – Lindelöf Argument and the Banach – Caccioppoli Contraction Mapping Principle","authors":"Alexander I. Bufetov,&nbsp;Ilya I. Zavolokin","doi":"10.1134/S1560354725040070","DOIUrl":"10.1134/S1560354725040070","url":null,"abstract":"<div><p>The aim of this note is to present a simple observation that a slight refinement of the\u0000contraction mapping principle allows one to recover the precise convergence rate in the\u0000Picard – Lindelöf theorem.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 Editors:","pages":"566 - 581"},"PeriodicalIF":0.8,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121365","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
Metric Geometry and Forced Oscillations in Mechanical Systems 机械系统中的度量几何和强迫振荡
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-08-11 DOI: 10.1134/S1560354725040173
Ivan Yu. Polekhin
{"title":"Metric Geometry and Forced Oscillations in Mechanical Systems","authors":"Ivan Yu. Polekhin","doi":"10.1134/S1560354725040173","DOIUrl":"10.1134/S1560354725040173","url":null,"abstract":"<div><p>We consider the problem of existence of forced oscillations on a Riemannian manifold, the metric on which is defined by the kinetic energy of a mechanical system. Under the assumption that the generalized forces are periodic functions of time, we find periodic solutions of the same period. We present sufficient conditions for the existence of such solutions, which essentially depend on the behavior of geodesics on the corresponding Riemannian manifold.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 Editors:","pages":"732 - 741"},"PeriodicalIF":0.8,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121755","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
Poncelet Porism in Singular Cases 奇异情况下的庞塞莱波律
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-08-11 DOI: 10.1134/S1560354725040094
Vladimir Dragović, Milena Radnović
{"title":"Poncelet Porism in Singular Cases","authors":"Vladimir Dragović,&nbsp;Milena Radnović","doi":"10.1134/S1560354725040094","DOIUrl":"10.1134/S1560354725040094","url":null,"abstract":"<div><p>The celebrated Poncelet porism is usually studied for a pair of smooth conics that are in a general position. Here we discuss Poncelet porism in the real plane — affine or projective, when that is not the case, i. e., the conics have at least one point of tangency or at least one of the conics is not smooth.\u0000In all such cases, we find necessary and sufficient conditions for the existence of an <span>(n)</span>-gon inscribed in one of the conics and circumscribed about the other.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 Editors:","pages":"598 - 611"},"PeriodicalIF":0.8,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121604","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
Infinite-Dimensional and Field-Theoretic Nonholonomic Mechanics 无限维场论非完整力学
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-08-11 DOI: 10.1134/S1560354725040069
Anthony M. Bloch, Dmitry V. Zenkov
{"title":"Infinite-Dimensional and Field-Theoretic Nonholonomic Mechanics","authors":"Anthony M. Bloch,&nbsp;Dmitry V. Zenkov","doi":"10.1134/S1560354725040069","DOIUrl":"10.1134/S1560354725040069","url":null,"abstract":"<div><p>Nonholonomic systems are mechanical systems with ideal velocity constraints that are not derivable from position constraints and with dynamics identified by the Lagrange – d’Alembert principle.\u0000This paper reviews infinite-dimensional and field-theoretic nonholonomic systems as well as Hamel’s formalism for these settings.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 Editors:","pages":"550 - 565"},"PeriodicalIF":0.8,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121779","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
Billiard Trajectories inside Cones 圆锥体内的台球轨迹
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-08-11 DOI: 10.1134/S156035472504015X
Andrey E. Mironov, Siyao Yin
{"title":"Billiard Trajectories inside Cones","authors":"Andrey E. Mironov,&nbsp;Siyao Yin","doi":"10.1134/S156035472504015X","DOIUrl":"10.1134/S156035472504015X","url":null,"abstract":"<div><p>Recently it was proved that every billiard trajectory inside a <span>(C^{3})</span> convex cone has a finite number of reflections. Here, by a <span>(C^{3})</span> convex cone, we mean a cone whose section with some hyperplane is a strictly convex, closed <span>(C^{3})</span> hypersurface of that hyperplane, with an everywhere nondegenerate second fundamental form. In this paper, we prove that there exist <span>(C^{2})</span> convex cones with billiard trajectories that undergo infinitely many reflections in finite time. We also provide an estimation of the number of reflections for billiard trajectories inside elliptic cones in <span>(mathbb{R}^{3})</span> using two first integrals.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 Editors:","pages":"688 - 710"},"PeriodicalIF":0.8,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121784","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
Real Analyticity of 2-Dimensional Superintegrable Metrics and Solution of Two Bolsinov – Kozlov – Fomenko Conjectures 二维超可积度量的实解析性及两个Bolsinov - Kozlov - Fomenko猜想的解
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-08-11 DOI: 10.1134/S1560354725040148
Vladimir S. Matveev
{"title":"Real Analyticity of 2-Dimensional Superintegrable Metrics and Solution of Two Bolsinov – Kozlov – Fomenko Conjectures","authors":"Vladimir S. Matveev","doi":"10.1134/S1560354725040148","DOIUrl":"10.1134/S1560354725040148","url":null,"abstract":"<div><p>We study two-dimensional Riemannian metrics which are superintegrable in the class of\u0000integrals polynomial in momenta.\u0000The study is based on our main technical result, Theorem 2, which states that the\u0000Poisson bracket of two integrals polynomial in momenta is an algebraic function of\u0000the integrals and of the Hamiltonian. We conjecture that two-dimensional superintegrable Riemannian metrics are necessarily real-analytic in isothermal coordinate systems, and give arguments supporting this conjecture. A small modification of the arguments, discussed in the paper, provides a method to construct new superintegrable systems. We prove a special case of the above conjecture which is sufficient to show that\u0000the metrics constructed by K. Kiyohara [9], which admit irreducible\u0000integrals polynomial in momenta, of arbitrary high degree <span>(k)</span>, are not superintegrable and\u0000in particular do not admit nontrivial integrals polynomial in momenta, of degree less\u0000than <span>(k)</span>. This result solves Conjectures (b) and (c) explicitly formulated in [4].</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 Editors:","pages":"677 - 687"},"PeriodicalIF":0.8,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121792","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
Singular KAM Theory for Convex Hamiltonian Systems 凸哈密顿系统的奇异KAM理论
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-08-11 DOI: 10.1134/S1560354725040057
Santiago Barbieri, Luca Biasco, Luigi Chierchia, Davide Zaccaria
{"title":"Singular KAM Theory for Convex Hamiltonian Systems","authors":"Santiago Barbieri,&nbsp;Luca Biasco,&nbsp;Luigi Chierchia,&nbsp;Davide Zaccaria","doi":"10.1134/S1560354725040057","DOIUrl":"10.1134/S1560354725040057","url":null,"abstract":"<div><p>In this note, we briefly discuss how the singular KAM theory of [7] — which was worked out for the mechanical case <span>(frac{1}{2}|y|^{2}+varepsilon f(x))</span> — can be extended to <i>convex</i> real-analytic\u0000nearly integrable Hamiltonian systems\u0000with Hamiltonian in action-angle variables given by <span>(h(y)+varepsilon f(x))</span> with <span>(h)</span> convex and\u0000<span>(f)</span> generic.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 Editors:","pages":"538 - 549"},"PeriodicalIF":0.8,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121692","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 Lorentzian Anti-de Sitter Plane 洛伦兹反德西特平面
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-08-11 DOI: 10.1134/S1560354725040045
Anton Z. Ali, Yuri L. Sachkov
{"title":"The Lorentzian Anti-de Sitter Plane","authors":"Anton Z. Ali,&nbsp;Yuri L. Sachkov","doi":"10.1134/S1560354725040045","DOIUrl":"10.1134/S1560354725040045","url":null,"abstract":"<div><p>In this paper the two-dimensional Lorentzian problem on the anti-de Sitter plane is studied. Using methods of geometric control theory and differential geometry, we describe the reachable set, investigate the existence of Lorentzian length maximizers, compute extremal trajectories, construct an optimal synthesis, characterize Lorentzian distance and spheres, and describe the Lie algebra of Killing vector fields.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 Editors:","pages":"504 - 537"},"PeriodicalIF":0.8,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121778","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 Tensor Invariants of the Clebsch System 关于Clebsch系统的张量不变量
IF 0.8 4区 数学
Regular and Chaotic Dynamics Pub Date : 2025-08-11 DOI: 10.1134/S1560354725040185
Andrey V. Tsiganov
{"title":"On Tensor Invariants of the Clebsch System","authors":"Andrey V. Tsiganov","doi":"10.1134/S1560354725040185","DOIUrl":"10.1134/S1560354725040185","url":null,"abstract":"<div><p>We present some new Poisson bivectors that are invariants by the Clebsch system flow. Symplectic integrators on their symplectic leaves exactly preserve the corresponding Casimir functions, which have different physical meanings. The Kahan discretization of the Clebsch system is discussed briefly.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 Editors:","pages":"742 - 764"},"PeriodicalIF":0.8,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121791","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信