A C1 generic condition for existence of symbolic extensions of volume preserving diffeomorphisms

被引：7
作者：
Catalan, Thiago [1 ]
机构：
[1] Univ Fed Uberlandia, Fac Matemat, BR-34323094 Uberlandia, MG, Brazil
来源：
NONLINEARITY | 2012年 / 25卷 / 12期
基金：
巴西圣保罗研究基金会;
关键词：
SMOOTH INTERVAL MAPS; HOMOCLINIC TANGENCIES; CONSERVATIVE-SYSTEMS; INVARIANT-MANIFOLDS; HYPERBOLICITY; STABILITY; DYNAMICS; POINTS; LEMMA;
D O I：
10.1088/0951-7715/25/12/3505
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that a C-1-generic volume preserving diffeomorphism has a symbolic extension if and only if this diffeomorphism is partial hyperbolic. This result is obtained by means of good dichotomies. In particular, we prove Bonatti's conjecture in the volume preserving scenario. More precisely, in the complement of Anosov diffeomorphisms we have densely robust heterodimensional cycles.
引用
收藏
页码：3505 / 3525
页数：21
相关论文
共 41 条
  • [1] Periodic points and homoclinic classes
    Abdenur, F.
    Bonatti, Ch.
    Crovisier, S.
    Diaz, L. J.
    Wen, L.
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2007, 27 : 1 - 22
  • [2] Arbieto A, 2012, ERGOD THEOR IN PRESS
  • [3] A pasting lemma and some applications for conservative systems
    Arbieto, Alexander
    Matheus, Carlos
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2007, 27 : 1399 - 1417
  • [4] On the regularization of conservative maps
    Avila, Artur
    [J]. ACTA MATHEMATICA, 2010, 205 (01) : 5 - 18
  • [5] Recurrence and genericty
    Bonatti, C
    Crovisier, S
    [J]. INVENTIONES MATHEMATICAE, 2004, 158 (01) : 33 - 104
  • [6] Persistent nonhyperbolic transitive diffeomorphisms
    Bonatti, C
    Diaz, LJ
    [J]. ANNALS OF MATHEMATICS, 1996, 143 (02) : 357 - 396
  • [7] A C1-generic dichotomy for diffeomorphisms:: Weak forms of hyperbolicity or infinitely many sinks or sources
    Bonatti, C
    Díaz, LJ
    Pujals, ER
    [J]. ANNALS OF MATHEMATICS, 2003, 158 (02) : 355 - 418
  • [8] Residual entropy, conditional entropy and subshift covers
    Boyle, M
    Fiebig, D
    Fiebig, U
    [J]. FORUM MATHEMATICUM, 2002, 14 (05) : 713 - 757
  • [9] Burguet D, 2012, SYMBOLIC EXTEN UNPUB
  • [10] Burguet D, 2012, ANN SCI ECOLE NORM S, V45, P337
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