Dynamics near nonhyperbolic fixed points or nontransverse homoclinic points

被引：0

作者：

Kryzhevich, Sergey ^{[1
]}

机构：

[1] St Petersburg State Univ, Fac Math & Mech, St Petersburg 198503, Russia

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2014年 / 95卷

关键词：

Partial hyperbolicity; Center unstable manifold; Homoclinic point; Chaos; PERIODIC POINTS; LYAPUNOV FUNCTIONS; SYSTEMS; ORBITS; BIFURCATIONS; PERSISTENCE; STABILITY;

D O I：

10.1016/j.matcom.2012.07.007

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We study dynamics in a neighborhood of a nonhyperbolic fixed point or an irreducible homoclinic tangent point. General type conditions for the existence of infinite sets of periodic points are obtained. A new method, based on the study of the dynamics of center disks, is introduced. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：163 / 179

页数：17

共 50 条

[1] THE TRANSVERSE HOMOCLINIC DYNAMICS AND THEIR BIFURCATIONS AT NONHYPERBOLIC FIXED-POINTS
DENG, B
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 331 (01) : 15 - 53
[2] SHADOWING NEAR NONHYPERBOLIC FIXED POINTS
Petrov, Alexey A.
Pilyugin, Sergei Yu.
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2014, 34 (09): : 3761 - 3772
[3] HOMOCLINIC POINTS NEAR ELLIPTIC FIXED-POINTS
ZEHNDER, E
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1973, 26 (02) : 131 - 182
[4] On the computation of nonhyperbolic fixed points
Graça, MM
[J]. EXPERIMENTAL MATHEMATICS, 2002, 11 (04) : 477 - 485
[5] FIXED-POINTS OF DIFFEOMORPHISM ITERATES NEAR HOMOCLINIC POINT
KAWAKAMI, H
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1973, 14 (03) : 442 - 461
[6] Hyperchaos in a Conservative System with Nonhyperbolic Fixed Points
Wu, Aiguo
Cang, Shijian
Zhang, Ruiye
Wang, Zenghui
Chen, Zengqiang
[J]. COMPLEXITY, 2018,
[7] Structure of stochastic dynamics near fixed points
Kwon, C
Ao, P
Thouless, DJ
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2005, 102 (37) : 13029 - 13033
[8] HOMOCLINIC POINTS NEAR DEGENERATE HOMOCLINICS
SCHALK, U
KNOBLOCH, J
[J]. NONLINEARITY, 1995, 8 (06) : 1133 - 1141
[9] The dynamics of holomorphic germs near a curve of fixed points
Sahroui, Fatiha
[J]. APPLIED MATHEMATICS LETTERS, 2008, 21 (12) : 1229 - 1233
[10] The Dynamics of Holomorphic Maps Near Curves of Fixed Points
Bracci, Filippo
[J]. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2003, 2 (03) : 493 - 520

← 1 2 3 4 5 →