Billiards: A singular perturbation limit of smooth Hamiltonian flows

被引：14

作者：

Rom-Kedar, V. ^{[1
]}

Turaev, D. ^{[2
]}

机构：

[1] Weizmann Inst Sci, Dept Math, Estrin Family Chair Comp Sci & Appl Math, IL-76910 Rehovot, Israel

[2] Univ London Imperial Coll Sci Technol & Med, Dept Math, London, England

来源：

CHAOS | 2012年 / 22卷 / 02期

基金：

英国工程与自然科学研究理事会; 以色列科学基金会;

关键词：

HARD BALL SYSTEMS; CHAOTIC SCATTERING; BOUNCE TRAJECTORIES; SOFT BILLIARDS; 1ST INTEGRALS; POTENTIALS; POINTS; NONEXISTENCE; ERGODICITY; MECHANICS;

D O I：

10.1063/1.4722010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Nonlinear multi-dimensional Hamiltonian systems that are not near integrable typically have mixed phase space and a plethora of instabilities. Hence, it is difficult to analyze them, to visualize them, or even to interpret their numerical simulations. We survey an emerging methodology for analyzing a class of such systems: Hamiltonians with steep potentials that limit to billiards. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4722010]

引用

页数：21

共 50 条

[11] Singular perturbation problems in a general smooth domain
Gie, Gung-Min
ASYMPTOTIC ANALYSIS, 2009, 62 (3-4) : 227 - 249
[12] The number of limit cycles of cubic Hamiltonian system with perturbation
Wu, Cheng-qiang
Xia, Yonghui
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2006, 7 (05) : 943 - 949
[13] The number of limit cycles of aquintic Hamiltonian system with perturbation
Atabaigi, Ali
Nyamoradi, Nemat
Zangeneh, Hamid R. Z.
BALKAN JOURNAL OF GEOMETRY AND ITS APPLICATIONS, 2008, 13 (02): : 1 - 11
[14] BRANCHING HAMILTONIAN BILLIARDS
VASILIEV, DG
SAFAROV, IG
DOKLADY AKADEMII NAUK SSSR, 1988, 301 (02): : 271 - 275
[15] Two-frequency perturbation of a smooth Hamiltonian system
Vecheslavov, VV
TECHNICAL PHYSICS, 2003, 48 (09) : 1079 - 1089
[16] Two-frequency perturbation of a smooth hamiltonian system
V. V. Vecheslavov
Technical Physics, 2003, 48 : 1079 - 1089
[17] Singular Limit of the Rotational Compressible Magnetohydrodynamic Flows
Kwon, Young-Sam
ADVANCES IN MATHEMATICAL PHYSICS, 2017, 2017
[18] Limit Behaviour of a Singular Perturbation Problem for the Biharmonic Operator
Serena Dipierro
Aram L. Karakhanyan
Enrico Valdinoci
Applied Mathematics & Optimization, 2019, 80 : 679 - 713
[19] Limit Behaviour of a Singular Perturbation Problem for the Biharmonic Operator
Dipierro, Serena
Karakhanyan, Aram L.
Valdinoci, Enrico
APPLIED MATHEMATICS AND OPTIMIZATION, 2019, 80 (03): : 679 - 713
[20] Smooth mixing flows with purely singular spectra
Fayad, B
DUKE MATHEMATICAL JOURNAL, 2006, 132 (02) : 371 - 391

← 1 2 3 4 5 →