Homoclinic bifurcations of endomorphisms: The codimension one case

被引：1
|
作者：
Mora, L [1 ]
机构：
[1] Inst Venezolano Invest Cient, Dept Matemat, Caracas 1020A, Venezuela
来源：
APPLIED MATHEMATICS LETTERS | 1998年 / 11卷 / 06期
关键词：
homoclinic bifurcations; endomorphisms;
D O I：
10.1016/S0893-9659(98)00107-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this note, we consider the dynamic that appears when we unfold a quadratic degenerate homoclinic point of a generic one-parameter family of endomorphisms f(mu). This is done through a rescaling technique. Among other facts, it follows from our theorem the abundance of strange expanding sets. (C) 1998 Elsevier Science Ltd. All rights reserved.
引用
收藏
页码：81 / 86
页数：6
相关论文
共 50 条
  • [1] Codimension 2 bifurcations of double homoclinic loops
    Zhang, Weipeng
    Zhu, Deming
    [J]. CHAOS SOLITONS & FRACTALS, 2009, 39 (01) : 295 - 303
  • [2] Numerical detection and continuation of saddle-node homoclinic bifurcations of codimension one and two
    Bai, FS
    Champneys, AR
    [J]. DYNAMICS AND STABILITY OF SYSTEMS, 1996, 11 (04): : 325 - 346
  • [3] On codimension one special Anosov endomorphisms
    Zhang, Xiang
    [J]. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2023, 38 (02): : 197 - 216
  • [4] Construction of codimension one homoclinic cycles
    Homburg, Ale Jan
    Kellner, Maria
    Knobloch, Juergen
    [J]. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2014, 29 (01): : 133 - 151
  • [5] NUMERICAL DETECTION AND CONTINUATION OF CODIMENSION-2 HOMOCLINIC BIFURCATIONS
    CHAMPNEYS, AR
    KUZNETSOV, YA
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1994, 4 (04): : 785 - 822
  • [6] Rational endomorphisms of codimension one holomorphic foliations
    Lo Bianco, Federico
    Pereira, Jorge Vitorio
    Rousseau, Erwan
    Touzet, Frederic
    [J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2022, 2022 (789): : 43 - 101
  • [7] The existence of infinitely many homoclinic doubling bifurcations from some codimension 3 homoclinic orbits
    Kokubu H.
    Naudot V.
    [J]. Journal of Dynamics and Differential Equations, 1997, 9 (3) : 445 - 462
  • [8] Codimension 3 Nontwisted Double Homoclinic Loops Bifurcations with Resonant Eigenvalues
    Weipeng Zhang
    Deming Zhu
    Dan Liu
    [J]. Journal of Dynamics and Differential Equations, 2008, 20 : 893 - 908
  • [9] Numerical unfoldings of codimension-three resonant homoclinic flip bifurcations
    Oldeman, BE
    Krauskopf, B
    Champneys, AR
    [J]. NONLINEARITY, 2001, 14 (03) : 597 - 621
  • [10] Codimension 3 nonresonant bifurcations of homoclinic orbits with two inclination flips
    SHUI Shuliang & ZHU Deming College of Mathematics and Physics
    Department of Mathematics
    [J]. Science China Mathematics, 2005, (02) : 248 - 260
12345