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
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
On the Uniqueness of Convex Central Configurations in the Planar (4)-Body Problem 平面体问题凸中心构型的唯一性
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-07-31 DOI: 10.1134/S1560354723520076
Shanzhong Sun, Zhifu Xie, Peng You
{"title":"On the Uniqueness of Convex Central Configurations in the Planar (4)-Body Problem","authors":"Shanzhong Sun,&nbsp;Zhifu Xie,&nbsp;Peng You","doi":"10.1134/S1560354723520076","DOIUrl":"10.1134/S1560354723520076","url":null,"abstract":"<div><p>In this paper, we provide a rigorous computer-assisted proof (CAP) of the conjecture that in the planar four-body problem there exists a unique convex central configuration for any four fixed positive masses in a given order belonging to a closed domain in the mass space. The proof employs the Krawczyk operator and the implicit function theorem (IFT). Notably, we demonstrate that the implicit function theorem can be combined with interval analysis, enabling us to estimate the size of the region where the implicit function exists and extend our findings from one mass point to its neighborhood.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 4","pages":"512 - 532"},"PeriodicalIF":1.4,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50528523","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
Aubry Set on Infinite Cyclic Coverings 无限循环覆盖上的Aubry集
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-07-31 DOI: 10.1134/S1560354723520015
Albert Fathi, Pierre Pageault
{"title":"Aubry Set on Infinite Cyclic Coverings","authors":"Albert Fathi,&nbsp;Pierre Pageault","doi":"10.1134/S1560354723520015","DOIUrl":"10.1134/S1560354723520015","url":null,"abstract":"<div><p>In this paper, we study the projected Aubry set of a lift of a Tonelli\u0000Lagrangian <span>(L)</span> defined on the tangent bundle of a compact manifold <span>(M)</span> to an infinite cyclic covering of <span>(M)</span>. Most of weak KAM and Aubry – Mather theory can be done in this setting. We give a necessary and sufficient condition for the emptiness of the projected Aubry set of the lifted Lagrangian involving both Mather minimizing measures and Mather classes of <span>(L)</span>. Finally, we give Mañè examples on the two-dimensional torus showing that our results do not necessarily hold when the cover is not infinite cyclic.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 4","pages":"425 - 446"},"PeriodicalIF":1.4,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50528657","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
From (2N) to Infinitely Many Escape Orbits 从（2N）到无穷多逃逸轨道
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-07-31 DOI: 10.1134/S1560354723520039
Josep Fontana-McNally, Eva Miranda, Cédric Oms, Daniel Peralta-Salas
{"title":"From (2N) to Infinitely Many Escape Orbits","authors":"Josep Fontana-McNally,&nbsp;Eva Miranda,&nbsp;Cédric Oms,&nbsp;Daniel Peralta-Salas","doi":"10.1134/S1560354723520039","DOIUrl":"10.1134/S1560354723520039","url":null,"abstract":"<div><p>In this short note, we prove that singular Reeb vector fields associated with generic <span>(b)</span>-contact forms on three dimensional manifolds with compact embedded critical surfaces have either (at least) <span>(2N)</span> or an infinite number of escape orbits, where <span>(N)</span> denotes the number of connected components of the critical set. In case where the first Betti number of a connected component of the critical surface is positive, there exist infinitely many escape orbits. A similar result holds in the case of <span>(b)</span>-Beltrami vector fields that are not <span>(b)</span>-Reeb. The proof is based on a more detailed analysis of the main result in [19].</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 4","pages":"498 - 511"},"PeriodicalIF":1.4,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50528522","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
Total Collision with Slow Convergence to a Degenerate Central Configuration 退化中心构型的慢收敛全碰撞
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-07-31 DOI: 10.1134/S1560354723040020
Richard Moeckel
{"title":"Total Collision with Slow Convergence to a Degenerate Central Configuration","authors":"Richard Moeckel","doi":"10.1134/S1560354723040020","DOIUrl":"10.1134/S1560354723040020","url":null,"abstract":"<div><p>For total collision solutions of the <span>(n)</span>-body problem, Chazy showed that the overall size of the configuration converges to zero with asymptotic rate proportional to <span>(|T-t|^{frac{2}{3}})</span> where <span>(T)</span> is the\u0000collision time. He also showed that the shape of the configuration converges to the set of\u0000central configurations. If the limiting central configuration is nondegenerate, the rate of convergence of the shape is of order <span>(O(|T-t|^{p}))</span> for some <span>(p&gt;0)</span>. Here we show by example that in the planar four-body\u0000problem there exist total collision solutions whose shape converges to a degenerate central configuration at a rate which is slower that any power of <span>(|T-t|)</span>.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 4","pages":"533 - 542"},"PeriodicalIF":1.4,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S1560354723040020.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50528524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Brake Orbits Fill the N-Body Hill Region 制动器轨道填充N型车身坡道区域
IF 1.4 4区 数学
Regular and Chaotic Dynamics Pub Date : 2023-07-31 DOI: 10.1134/S1560354723520027
Richard Montgomery
{"title":"Brake Orbits Fill the N-Body Hill Region","authors":"Richard Montgomery","doi":"10.1134/S1560354723520027","DOIUrl":"10.1134/S1560354723520027","url":null,"abstract":"<div><p>A brake orbit for the N-body problem is a solution for which, at some instant,\u0000all velocities of all bodies are zero. We reprove two “lost theorems” regarding brake orbits and use them to establish some surprising properties of the completion of the\u0000Jacobi – Maupertuis metric for the N-body problem at negative energies.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 4","pages":"374 - 394"},"PeriodicalIF":1.4,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50528651","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：481959085
Book学术官方微信