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.
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页码：3505 / 3525
页数：21
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