Partial hyperbolicity and homoclinic tangencies

被引：27

作者：

Crovisier, Sylvain ^{[1
]}

Sambarino, Martin ^{[2
]}

Yang, Dawei ^{[3
]}

机构：

[1] Univ Paris 11, CNRS, Lab Math Orsay, UMR 8628, Bat 425, F-91405 Orsay, France

[2] Univ Republica, Fac Ciencias, CMAT, Montevideo 11400, Uruguay

[3] Soochow Univ, Sch Math Sci, Suzhou 215006, Peoples R China

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2015年 / 17卷 / 01期

关键词：

Homoclinic tangency; heterodimensional cycle; hyperbolic diffeomorphism; generic dynamics; homoclinic class; partial hyperbolicity; ENTROPY; STABILITY; SETS;

D O I：

10.4171/JEMS/497

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that any diffeomorphism of a compact manifold can be C-1 approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic structure.

引用

页码：1 / 49

页数：49

共 50 条

[1] Homoclinic tangencies and hyperbolicity for surface diffeomorphisms
Pujals, ER
Sambarino, M
ANNALS OF MATHEMATICS, 2000, 151 (03) : 961 - 1023
[2] On homoclinic tangencies, hyperbolicity, creation of homoclinic orbits and variation of entropy
Pujals, ER
Sambarino, M
NONLINEARITY, 2000, 13 (03) : 921 - 926
[3] Unfolding homoclinic tangencies inside horseshoes: hyperbolicity, fractal dimensions and persistent tangencies
Rios, IL
NONLINEARITY, 2001, 14 (03) : 431 - 462
[4] Homoclinic tangencies versus uniform hyperbolicity for conservative 3-flows
Bessa, Mario
Rocha, Jorge
JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 247 (11) : 2913 - 2923
[5] Partial hyperbolicity far from homoclinic bifurcations
Crovisier, Sylvain
ADVANCES IN MATHEMATICS, 2011, 226 (01) : 673 - 726
[6] Homoclinic tangencies in Rn
Rayskin, V
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2005, 12 (03) : 465 - 480
[7] Quasiattractors and homoclinic tangencies
Gonchenko, SV
Shilnikov, LP
Turaev, DV
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1997, 34 (2-4) : 195 - 227
[8] Hopf bifurcations and homoclinic tangencies
Martín, JC
NONLINEARITY, 1999, 12 (04) : 893 - 902
[9] Homoclinic tangencies and dominated splittings
Wen, L
NONLINEARITY, 2002, 15 (05) : 1445 - 1469
[10] Rigorous computations of homoclinic tangencies
Arai, Zin
Mischaikow, Konstantin
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2006, 5 (02): : 280 - 292

← 1 2 3 4 5 →