Generic diffieomorphisms away from homoclinic tangencies and heterodimensional cycles

被引：46
|
作者：
Wen, L [1 ]
机构：
[1] Peking Univ, Sch Math, Beijing 100871, Peoples R China
来源：
BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY | 2004年 / 35卷 / 03期
基金：
中国国家自然科学基金;
关键词：
hyperbolic diffeomorphism; homoclinic tangency; heterodimensional cycle; generic property; dominated splitting;
D O I：
10.1007/s00574-004-0023-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The C-1 density conjecture of Palis asserts that diffeomorphisms exhibiting either a homoclinic tangency or a heterodimensional cycle are C-1 dense in the complement of the C-1 closure of hyperbolic systems. In this paper we prove some results towards the conjecture.
引用
收藏
页码：419 / 452
页数：34
相关论文
共 12 条
  • [1] Generic diffeomorphisms away from homoclinic tangencies and heterodimensional cycles
    Lan Wen*
    Bulletin of the Brazilian Mathematical Society, 2004, 35 : 419 - 452
  • [2] Homoclinic tangencies leading to robust heterodimensional cycles
    Barrientos, Pablo G.
    Diaz, Lorenzo J.
    Perez, Sebastian A.
    MATHEMATISCHE ZEITSCHRIFT, 2022, 302 (01) : 519 - 558
  • [3] Homoclinic tangencies leading to robust heterodimensional cycles
    Pablo G. Barrientos
    Lorenzo J. Díaz
    Sebastián A. Pérez
    Mathematische Zeitschrift, 2022, 302 : 519 - 558
  • [4] NONTRANSVERSE HETERODIMENSIONAL CYCLES: STABILISATION AND ROBUST TANGENCIES
    Diaz, Lorenzo J.
    Perez, Sebastian A.
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2022,
  • [5] NONTRANSVERSE HETERODIMENSIONAL CYCLES: STABILISATION AND ROBUST TANGENCIES
    Diaz, Lorenzo J.
    Perez, Sebastian A.
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2023, 376 (02) : 891 - 944
  • [6] PERSISTENT HOMOCLINIC TANGENCIES AND THE UNFOLDING OF CYCLES
    DIAZ, LJ
    URES, R
    ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1994, 11 (06): : 643 - 659
  • [7] Hopf-homoclinic Bifurcations and Heterodimensional Cycles
    Tomizawa, Shuntaro
    TOKYO JOURNAL OF MATHEMATICS, 2019, 42 (02) : 449 - 469
  • [8] Robust heterodimensional cycles and C1-generic dynamics
    Bonatti, Christian
    Diaz, Lorenzo J.
    JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 2008, 7 (03) : 469 - 525
  • [9] How do hyperbolic homoclinic classes collide at heterodimensional cycles
    Diaz, Lorenzo J.
    Rocha, Jorge
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2007, 17 (03) : 589 - 627
  • [10] Purely imaginary eigenvalues from homoclinic tangencies
    Morales, C. A.
    APPLIED MATHEMATICS LETTERS, 2012, 25 (11) : 2005 - 2008
12