Splitting of separatrices: perturbation theory and exponential smallness

被引：46
作者：
Gelfreich, VG [1 ]
Lazutkin, VF [1 ]
机构：
[1] St Petersburg State Univ, St Petersburg 198904, Russia
来源：
RUSSIAN MATHEMATICAL SURVEYS | 2001年 / 56卷 / 03期
关键词：
D O I：
10.1070/RM2001v056n03ABEH000394
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This is a survey of the main results related to separatrix splitting for area-preserving maps and Hamiltonian systems with one and a half degrees of freedom. Special attention is paid to problems in which the separatrix splitting is exponentially small with respect to the perturbation parameter.
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收藏
页码：499 / 558
页数：60
相关论文
共 90 条
  • [1] ALEKSEEV VM, 1969, MATH USSR SB, V7, P1
  • [2] BEYOND ALL ORDERS - SINGULAR PERTURBATIONS IN A MAPPING
    AMICK, C
    CHING, ESC
    KADANOFF, LP
    ROMKEDAR, V
    [J]. JOURNAL OF NONLINEAR SCIENCE, 1992, 2 (01) : 9 - 67
  • [3] [Anonymous], 1993, KAM THEORY SEMICLASS
  • [4] [Anonymous], TOPICS MODERN PHYS T
  • [5] [Anonymous], LOND MATH S
  • [6] ARNOLD VI, 1964, DOKL AKAD NAUK SSSR+, V156, P9
  • [7] ARNOLD VI, 1985, SER SOVREM PROBL MAT, V3
  • [8] Bogolyubov N.N., 1974, ASYMPTOTIC METHODS T
  • [9] AN ASYMPTOTIC SYMMETRY OF THE RAPIDLY FORCED PENDULUM
    CHANG, YH
    SEGUR, H
    [J]. PHYSICA D-NONLINEAR PHENOMENA, 1991, 51 (1-3) : 109 - 118
  • [10] CHANG YH, 1991, NATO ADV SCI I B-PHY, V284, P213
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