Regular and Chaotic Dynamics最新文献_第3页

Non-Resonant Conditions for the Klein – Gordon Equation on the Circle 圆上克莱因-戈登方程的非共振条件

IF 0.8 4区数学

Regular and Chaotic Dynamics Pub Date : 2024-08-04 DOI: 10.1134/S1560354724040026

Roberto Feola, Jessica Elisa Massetti

引用次数: 0

On Elliptic Lower-Dimensional Invariant Tori with Prescribed Frequencies in Hamiltonian Systems with Small Parameters 论小参数哈密顿系统中具有规定频率的椭圆形低维不变矩阵

IF 0.8 4区数学

Regular and Chaotic Dynamics Pub Date : 2024-08-04 DOI: 10.1134/S156035472404004X

Hanru Zou, Junxiang Xu

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3D Orbital Architecture of Exoplanetary Systems: KAM-Stability Analysis 系外行星系统的 3D 轨道结构：KAM 稳定性分析

IF 0.8 4区数学

Regular and Chaotic Dynamics Pub Date : 2024-08-04 DOI: 10.1134/S1560354724040038

Chiara Caracciolo, Ugo Locatelli, Marco Sansottera, Mara Volpi

{"title":"3D Orbital Architecture of Exoplanetary Systems: KAM-Stability Analysis","authors":"Chiara Caracciolo, Ugo Locatelli, Marco Sansottera, Mara Volpi","doi":"10.1134/S1560354724040038","DOIUrl":"10.1134/S1560354724040038","url":null,"abstract":"<div>We study the KAM-stability of several single star two-planet\u0000nonresonant extrasolar systems. It is likely that the observed\u0000exoplanets are the most massive of the system considered. Therefore,\u0000their robust stability is a crucial and necessary condition for the\u0000long-term survival of the system when considering potential\u0000additional exoplanets yet to be seen. Our study is based on the\u0000construction of a combination of lower-dimensional elliptic and KAM\u0000tori, so as to better approximate the dynamics in the framework of\u0000accurate secular models. For each extrasolar system, we explore the\u0000parameter space of both inclinations: the one with respect to the\u0000line of sight and the mutual inclination between the planets. Our\u0000approach shows that remarkable inclinations, resulting in\u0000three-dimensional architectures that are far from being coplanar,\u0000can be compatible with the KAM stability of the system. We find\u0000that the highest values of the mutual inclinations are comparable to\u0000those of the few systems for which the said inclinations are determined\u0000by the observations.</div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Treschev)","pages":"565 - 582"},"PeriodicalIF":0.8,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S1560354724040038.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141935476","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

Persistence of Multiscale Degenerate Invariant Tori in Reversible Systems with Degenerate Frequency Mapping 具有退化频率映射的可逆系统中多尺度退化不变环的持续性

IF 0.8 4区数学

Regular and Chaotic Dynamics Pub Date : 2024-08-04 DOI: 10.1134/S1560354724040051

Xiaomei Yang, Junxiang Xu

引用次数: 0

Erratum to: Isolated Diophantine Numbers 勘误：孤立二阶数

IF 0.8 4区数学

Regular and Chaotic Dynamics Pub Date : 2024-07-17 DOI: 10.1134/S1560354724550033

Fernando Argentieri, Luigi Chierchia

引用次数: 0

Isolated Diophantine Numbers 孤立二阶数

IF 0.8 4区数学

Regular and Chaotic Dynamics Pub Date : 2024-07-05 DOI: 10.1134/S156035472455001X

Fernando Argentieri, Luigi Chierchia

引用次数: 0

Nineteen Fifty-Four: Kolmogorov’s New “Metrical Approach” to Hamiltonian Dynamics 19 54：科尔莫戈罗夫的汉密尔顿动力学新 "韵律方法

IF 0.8 4区数学

Regular and Chaotic Dynamics Pub Date : 2024-07-05 DOI: 10.1134/S1560354724550021

Luigi Chierchia, Isabella Fascitiello

引用次数: 0

KAM for Vortex Patches 用于涡流补丁的 KAM

IF 0.8 4区数学

Regular and Chaotic Dynamics Pub Date : 2024-06-21 DOI: 10.1134/S1560354724540013

Massimiliano Berti

{"title":"KAM for Vortex Patches","authors":"Massimiliano Berti","doi":"10.1134/S1560354724540013","DOIUrl":"10.1134/S1560354724540013","url":null,"abstract":"<div>In the last years substantial mathematical progress has been made in KAM theory\u0000for quasi-linear/fully nonlinear\u0000Hamiltonian partial differential equations, notably for\u0000water waves and Euler equations.\u0000In this survey we focus on recent advances in quasi-periodic vortex patch\u0000solutions of the (2d)-Euler equation in (mathbb{R}^{2})\u0000close to uniformly rotating Kirchhoff elliptical vortices,\u0000with aspect ratios belonging to a set of asymptotically full Lebesgue measure.\u0000The problem is reformulated into a quasi-linear Hamiltonian equation for a radial displacement from the ellipse. A major difficulty of the KAM proof is the presence of a zero normal mode frequency, which is due to the conservation of the angular momentum. The key novelty to overcome this degeneracy is to perform a perturbative symplectic reduction of the angular momentum, introducing it as a symplectic variable in the spirit of the Darboux – Carathéodory theorem of symplectic rectification, valid in finite dimension.\u0000This approach is particularly delicate in an infinite-dimensional phase space: our symplectic\u0000change of variables is a nonlinear modification of the transport flow generated by the angular\u0000momentum itself.</div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Treschev)","pages":"654 - 676"},"PeriodicalIF":0.8,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501790","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

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