Conservative homoclinic bifurcations and some applications

被引：3

作者：

Gorodetski, Anton ^{[1
]}

Kaloshin, Vadim ^{[2
]}

机构：

[1] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

[2] Penn State Univ, Dept Math, State Coll, PA 16802 USA

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2009年 / 267卷 / 01期

基金：

美国国家科学基金会;

关键词：

AREA-PRESERVING MAPS; RESTRICTED 3-BODY PROBLEM; DYNAMICAL-SYSTEMS; SITNIKOV PROBLEM; ELLIPTIC ISLES; SEPARATRICES; POINTS; DIFFEOMORPHISMS; TANGENCIES; ABUNDANCE;

D O I：

10.1134/S0081543809040063

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study generic unfoldings of homoclinic tangencies of two-dimensional area-preserving diffeomorphisms (conservative New house phenomena) and show that they give rise to invariant hyperbolic sets of arbitrarily large Hausdorff dimension. As applications, we discuss the size of the stochastic layer of a standard map and the Hausdorff dimension of invariant hyperbolic sets for certain restricted three-body problems. We avoid involved technical details and only concentrate on the ideas of the proof of the presented results.

引用

页码：76 / 90

页数：15

共 50 条

[31] Exponentially small separatrix splittings and almost invisible homoclinic bifurcations in some billiard tables
Ramírez-Ros, R
[J]. PHYSICA D-NONLINEAR PHENOMENA, 2005, 210 (3-4) : 149 - 179
[32] HOMOCLINIC POINTS IN CONSERVATIVE SYSTEMS
TAKENS, F
[J]. INVENTIONES MATHEMATICAE, 1972, 18 (3-4) : 267 - 292
[33] Predicting Homoclinic Bifurcations in Planar Autonomous Systems
Mohamed Belhaq
Faouzi Lakrad
Abdelhak Fahsi
[J]. Nonlinear Dynamics, 1999, 18 : 303 - 310
[34] Homoclinic bifurcations of endomorphisms: The codimension one case
Mora, L
[J]. APPLIED MATHEMATICS LETTERS, 1998, 11 (06) : 81 - 86
[35] Homoclinic bifurcations in self-excited oscillators
Belhaq, M
Fahsi, A
[J]. MECHANICS RESEARCH COMMUNICATIONS, 1996, 23 (04) : 381 - 386
[36] On the number of limit cycles in double homoclinic bifurcations
Han, M
Chen, J
[J]. SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY, 2000, 43 (09): : 914 - 928
[37] SUBSIDIARY BIFURCATIONS NEAR BIFOCAL HOMOCLINIC ORBITS
GLENDINNING, P
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1989, 105 : 597 - 605
[38] Predicting homoclinic bifurcations in planar autonomous systems
Belhaq, M
Lakrad, F
Fahsi, A
[J]. NONLINEAR DYNAMICS, 1999, 18 (04) : 303 - 310
[39] NONUNIVERSAL ACCUMULATION OF BIFURCATIONS LEADING TO HOMOCLINIC TANGENCY
DAIDO, H
[J]. PROGRESS OF THEORETICAL PHYSICS, 1983, 69 (04): : 1304 - 1307
[40] Homoclinic flip bifurcations accompanied by transcritical bifurcation
Xingbo Liu
[J]. Chinese Annals of Mathematics, Series B, 2011, 32 : 905 - 916

← 1 2 3 4 5 →