Asymptotic statistics of Poincare recurrences in Hamiltonian systems with divided phase space

被引：83

作者：

Chirikov, BV ^{[1
]}

Shepelyansky, DL

机构：

[1] Univ Toulouse 3, CNRS, UMR 5626, Phys Quant Lab, F-31062 Toulouse 4, France

[2] Budker Inst Nucl Phys, Novosibirsk 630090, Russia

来源：

PHYSICAL REVIEW LETTERS | 1999年 / 82卷 / 03期

关键词：

D O I：

10.1103/PhysRevLett.82.528

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

By different methods we show that for dynamical chaos in the standard map with critical golden curve, the Poincare recurrences P(tau) and correlations C(tau) decay asymptotically in time as P proportional to C/tau proportional to 1/tau(3). It is also explained why this asymptotic behavior starts only at very large times. We argue that the same exponent p = 3 should be also valid for a general chaos border. [S0031-9007(98)08272-6].

引用

页码：528 / 531

页数：4

共 50 条

[31] The Poincare bifurcation by perturbing a class of cubic Hamiltonian systems
Chang, Yuan
Zhao, Liqin
Wang, Qiuyi
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2025, 82
[32] ON THE STABILITY OF POINCARE PERIODIC SOLUTIONS OF HAMILTONIAN SYSTEMS.
Saitbattalov, A.A.
Journal of Applied Mathematics and Mechanics, 1984, 48 (02) : 146 - 150
[33] HAMILTONIAN PATH INTEGRAL FOR SYSTEMS WITH CONIC PHASE-SPACE
PROKHOROV, LV
SHABANOV, SV
VESTNIK LENINGRADSKOGO UNIVERSITETA SERIYA FIZIKA KHIMIYA, 1988, (01): : 68 - 71
[34] The Classical Action as a Tool to Visualise the Phase Space of Hamiltonian Systems
Montoya, Francisco Gonzalez
DYNAMICS, 2023, 3 (04): : 678 - 694
[35] Phase space flows for non-Hamiltonian systems with constraints
Sergi, A
PHYSICAL REVIEW E, 2005, 72 (03):
[36] Collapse of hierarchical phase space and mixing rates in Hamiltonian systems
Oliveira, Tulio M.
Artuso, Roberto
Manchein, Cesar
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2019, 530
[37] Transport in Hamiltonian systems with slowly changing phase space structure
Bouchet, Freddy
Woillez, Eric
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2020, 80
[38] Phase-space metric for non-Hamiltonian systems
Tarasov, VE
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2005, 38 (10): : 2145 - 2155
[39] On asymptotic Hopf invariant for Hamiltonian systems
Deryabin, MV
JOURNAL OF MATHEMATICAL PHYSICS, 2005, 46 (06)
[40] ASYMPTOTIC ANALYSIS OF HAMILTONIAN-SYSTEMS
VERHULST, F
LECTURE NOTES IN MATHEMATICS, 1983, 985 : 137 - 183

← 1 2 3 4 5 →