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Regular and Chaotic Dynamics最新文献

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Compactification of the Energy Surfaces for (n) Bodies 物体能量表面的紧致化
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-10-20 DOI: 10.1134/S1560354723040081
Andreas Knauf, Richard Montgomery
{"title":"Compactification of the Energy Surfaces for (n) Bodies","authors":"Andreas Knauf,&nbsp;Richard Montgomery","doi":"10.1134/S1560354723040081","DOIUrl":"10.1134/S1560354723040081","url":null,"abstract":"<div><p>For <span>(n)</span> bodies moving in Euclidean <span>(d)</span>-space under the influence of a\u0000homogeneous pair interaction we\u0000compactify every center of mass energy surface, obtaining a\u0000<span>(big{(}2d(n-1)-1big{)})</span>-dimensional manifold with corners in the sense of Melrose.\u0000After a time change, the flow on this manifold is globally defined\u0000and nontrivial on the boundary.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 4","pages":"628 - 658"},"PeriodicalIF":1.4,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50500791","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: 1
A Simple Proof of Gevrey Estimates for Expansions of Quasi-Periodic Orbits: Dissipative Models and Lower-Dimensional Tori 拟周期轨道展开的Gevrey估计的一个简单证明：耗散模型和低维Tori
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-10-20 DOI: 10.1134/S1560354723040123
Adrián P. Bustamante, Rafael de la Llave
{"title":"A Simple Proof of Gevrey Estimates for Expansions of Quasi-Periodic Orbits: Dissipative Models and Lower-Dimensional Tori","authors":"Adrián P. Bustamante,&nbsp;Rafael de la Llave","doi":"10.1134/S1560354723040123","DOIUrl":"10.1134/S1560354723040123","url":null,"abstract":"<div><p>We consider standard-like/Froeschlé dissipative maps\u0000with a dissipation and nonlinear perturbation. That is,\u0000</p>\u0000 <div><div><span>\u0000$$T_{varepsilon}(p,q)=left((1-gammavarepsilon^{3})p+mu+varepsilon V^{prime}(q),q+(1-gammavarepsilon^{3})p+mu+varepsilon V^{prime}(q)bmod 2piright)$$\u0000</span></div></div>\u0000 <p>\u0000where <span>(pin{mathbb{R}}^{D})</span>, <span>(qin{mathbb{T}}^{D})</span> are the dynamical\u0000variables. We fix a frequency <span>(omegain{mathbb{R}}^{D})</span> and study the existence of\u0000quasi-periodic orbits. When there is dissipation, having\u0000a quasi-periodic orbit of frequency <span>(omega)</span> requires\u0000selecting the parameter <span>(mu)</span>, called <i>the drift</i>.</p><p>We first study the Lindstedt series (formal power series in <span>(varepsilon)</span>) for quasi-periodic orbits with <span>(D)</span> independent frequencies and the drift when <span>(gammaneq 0)</span>.\u0000We show that, when <span>(omega)</span> is\u0000irrational, the series exist to all orders, and when <span>(omega)</span> is Diophantine,\u0000we show that the formal Lindstedt series are Gevrey.\u0000The Gevrey nature of the Lindstedt series above was shown\u0000in [3] using a more general method, but the present proof is\u0000rather elementary.</p><p>We also study the case when <span>(D=2)</span>, but the quasi-periodic orbits\u0000have only one independent frequency (lower-dimensional tori).\u0000Both when <span>(gamma=0)</span> and when <span>(gammaneq 0)</span>, we show\u0000that, under some mild nondegeneracy conditions on <span>(V)</span>, there\u0000are (at least two) formal Lindstedt series defined to all orders\u0000and that they are Gevrey.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 4","pages":"707 - 730"},"PeriodicalIF":1.4,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50500793","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 Families of Bowen – Series-Like Maps for Surface Groups 关于曲面群的类Bowen级数映射族
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-10-20 DOI: 10.1134/S1560354723040093
Lluís Alsedà, David Juher, Jérôme Los, Francesc Mañosas
{"title":"On Families of Bowen – Series-Like Maps for Surface Groups","authors":"Lluís Alsedà,&nbsp;David Juher,&nbsp;Jérôme Los,&nbsp;Francesc Mañosas","doi":"10.1134/S1560354723040093","DOIUrl":"10.1134/S1560354723040093","url":null,"abstract":"<div><p>We review some recent results on a class of maps, called Bowen – Series-like maps, obtained from a class of group presentations for surface groups. These maps are piecewise homeomorphisms of the circle with finitely many discontinuities. The topological entropy of each map in the class and its relationship with the growth function of the group presentation is discussed, as well as the computation of these invariants.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 4","pages":"659 - 667"},"PeriodicalIF":1.4,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50462505","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 Lambert Problem with Drag 关于具有阻力的Lambert问题
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-10-20 DOI: 10.1134/S156035472304010X
Antonio J. Ureña
{"title":"On the Lambert Problem with Drag","authors":"Antonio J. Ureña","doi":"10.1134/S156035472304010X","DOIUrl":"10.1134/S156035472304010X","url":null,"abstract":"<div><p>The Lambert problem consists in connecting two given points in a given lapse of time under the gravitational influence of a fixed center. While this problem is very classical, we are concerned here with situations where friction forces act alongside the Newtonian attraction. Under some boundedness assumptions on the friction, there exists exactly one rectilinear solution if the two points lie on the same ray, and at least two solutions traveling in opposite directions otherwise.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 4","pages":"668 - 689"},"PeriodicalIF":1.4,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50464491","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 Siegel – Bruno Linearization Theorem Siegel–Bruno线性化定理
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-10-20 DOI: 10.1134/S1560354723040147
Patrick Bernard
{"title":"The Siegel – Bruno Linearization Theorem","authors":"Patrick Bernard","doi":"10.1134/S1560354723040147","DOIUrl":"10.1134/S1560354723040147","url":null,"abstract":"<div><p>The purpose of this paper is a pedagogical one. We provide a short and self-contained account of Siegel’s theorem, as improved by Bruno, which states that a holomorphic map of the complex plane can be locally linearized near a fixed point under certain conditions on the multiplier. The main proof is adapted from Bruno’s work.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 4","pages":"756 - 762"},"PeriodicalIF":1.4,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50500795","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
Distance Estimates for Action-Minimizing Solutions of the (N)-Body Problem 一类（N）体问题的最小作用解的距离估计
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-10-20 DOI: 10.1134/S1560354723040044
Kuo-Chang Chen, Bo-Yu Pan
{"title":"Distance Estimates for Action-Minimizing Solutions of the (N)-Body Problem","authors":"Kuo-Chang Chen,&nbsp;Bo-Yu Pan","doi":"10.1134/S1560354723040044","DOIUrl":"10.1134/S1560354723040044","url":null,"abstract":"<div><p>In this paper we provide estimates for mutual distances of periodic solutions for the Newtonian <span>(N)</span>-body problem.\u0000Our estimates are based on masses, total variations of turning angles for relative positions, and predetermined upper bounds for\u0000action values. Explicit formulae will be proved by iterative arguments.\u0000We demonstrate some applications to action-minimizing solutions for three- and four-body problems.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 4","pages":"561 - 577"},"PeriodicalIF":1.4,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50435118","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
A Remark on the Onset of Resonance Overlap 关于共振重叠发生的一点注记
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-10-20 DOI: 10.1134/S1560354723040056
Jacques Fejoz, Marcel Guardia
{"title":"A Remark on the Onset of Resonance Overlap","authors":"Jacques Fejoz,&nbsp;Marcel Guardia","doi":"10.1134/S1560354723040056","DOIUrl":"10.1134/S1560354723040056","url":null,"abstract":"<div><p>Chirikov’s celebrated criterion of resonance overlap has been widely used in celestial mechanics and Hamiltonian dynamics to detect global instability, but is rarely rigorous. We introduce two simple Hamiltonian systems, each depending on two parameters measuring, respectively, the distance to resonance overlap and nonintegrability. Within some thin region of the parameter plane, classical perturbation theory shows the existence of global instability and symbolic dynamics, thus illustrating Chirikov’s criterion.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 4","pages":"578 - 584"},"PeriodicalIF":1.4,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50435119","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
Normalization Flow 归一化流程
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-10-20 DOI: 10.1134/S1560354723040160
Dmitry V. Treschev
{"title":"Normalization Flow","authors":"Dmitry V. Treschev","doi":"10.1134/S1560354723040160","DOIUrl":"10.1134/S1560354723040160","url":null,"abstract":"<div><p>We propose a new approach to the theory of normal forms for Hamiltonian systems near a nonresonant elliptic singular point. We consider the space of all Hamiltonian functions with such an equilibrium position at the origin and construct a differential equation in this space. Solutions of this equation move Hamiltonian functions towards their normal forms. Shifts along the flow of this equation correspond to canonical coordinate changes. So, we have a continuous normalization procedure. The formal aspect of the theory presents no difficulties.\u0000As usual, the analytic aspect and the problems of convergence of series are nontrivial.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 4","pages":"781 - 804"},"PeriodicalIF":1.4,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50500678","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: 1
Linear Stability of an Elliptic Relative Equilibrium in the Spatial (n)-Body Problem via Index Theory 用指数理论研究空间体问题中椭圆相对平衡的线性稳定性
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-10-20 DOI: 10.1134/S1560354723040135
Xijun Hu, Yuwei Ou, Xiuting Tang
{"title":"Linear Stability of an Elliptic Relative Equilibrium in the Spatial (n)-Body Problem via Index Theory","authors":"Xijun Hu,&nbsp;Yuwei Ou,&nbsp;Xiuting Tang","doi":"10.1134/S1560354723040135","DOIUrl":"10.1134/S1560354723040135","url":null,"abstract":"<div><p>It is well known that a planar central configuration of the <span>(n)</span>-body problem gives rise to a solution where each\u0000particle moves in a Keplerian orbit with a common eccentricity <span>(mathfrak{e}in[0,1))</span>. We call\u0000this solution an elliptic\u0000relative equilibrium (ERE for short). Since each particle of the ERE is always in the same\u0000plane, it is natural to regard\u0000it as a planar <span>(n)</span>-body problem. But in practical applications, it is more meaningful to\u0000consider the ERE as a spatial <span>(n)</span>-body problem (i. e., each particle belongs to <span>(mathbb{R}^{3})</span>).\u0000In this paper, as a spatial <span>(n)</span>-body problem, we first decompose the linear system of ERE into\u0000two parts, the planar and the spatial part.\u0000Following the Meyer – Schmidt coordinate [19], we give an expression for the spatial part and\u0000further obtain a rigorous analytical method to study the linear stability of\u0000the spatial part by the Maslov-type index theory. As an application, we obtain stability results for some classical ERE, including the\u0000elliptic Lagrangian solution, the Euler solution and the <span>(1+n)</span>-gon solution.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 4","pages":"731 - 755"},"PeriodicalIF":1.4,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50500794","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
Hamiltonian Paradifferential Birkhoff Normal Form for Water Waves 水波的Hamiltonian准微分Birkhoff正规形式
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-10-20 DOI: 10.1134/S1560354723040032
Massimiliano Berti, Alberto Maspero, Federico Murgante
{"title":"Hamiltonian Paradifferential Birkhoff Normal Form for Water Waves","authors":"Massimiliano Berti,&nbsp;Alberto Maspero,&nbsp;Federico Murgante","doi":"10.1134/S1560354723040032","DOIUrl":"10.1134/S1560354723040032","url":null,"abstract":"<div><p>We present the almost global in time existence result in [13]\u0000of small amplitude space <i>periodic</i>\u0000solutions of the 1D gravity-capillary water waves equations with constant vorticity\u0000and we describe the ideas of proof.\u0000This is based on a novel Hamiltonian paradifferential\u0000Birkhoff normal form approach for quasi-linear PDEs.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 4","pages":"543 - 560"},"PeriodicalIF":1.4,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50501020","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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