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

页码：3505 / 3525

页数：21

共 41 条

[1] Periodic points and homoclinic classes [J].

Abdenur, F. ;

Bonatti, Ch. ;

Crovisier, S. ;

Diaz, L. J. ;

Wen, L. .

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 [J].

Arbieto, Alexander ;

Matheus, Carlos .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2007, 27 :1399-1417

[4] On the regularization of conservative maps [J].

Avila, Artur .

ACTA MATHEMATICA, 2010, 205 (01) :5-18

[5] Recurrence and genericty [J].

Bonatti, C ;

Crovisier, S .

INVENTIONES MATHEMATICAE, 2004, 158 (01) :33-104

[6] Persistent nonhyperbolic transitive diffeomorphisms [J].

Bonatti, C ;

Diaz, LJ .

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 [J].

Bonatti, C ;

Díaz, LJ ;

Pujals, ER .

ANNALS OF MATHEMATICS, 2003, 158 (02) :355-418

[8] Residual entropy, conditional entropy and subshift covers [J].

Boyle, M ;

Fiebig, D ;

Fiebig, U .

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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