Connectedness of the Set of Central Lyapunov Exponents

被引：0

作者：

Fakhari, Abbas ^{[1
]}

Khalaj, Maryam ^{[1
]}

机构：

[1] Shahid Beheshti Univ, Dept Math, Tehran 19839, Iran

来源：

JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS | 2024年 / 30卷 / 04期

基金：

美国国家科学基金会; 中国国家自然科学基金;

关键词：

Homoclinic class; Partially hyperbolic; Lyapunov exponent; C1-generic; HYPERBOLICITY; CRITERION;

D O I：

10.1007/s10883-024-09718-9

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We show that there is a residual subsetRofDiff1(M)such that for anyf is an element of Rand anypartially hyperbolic homoclinic classH(p,f)with one-dimensional central direction, theset of central Lyapunov exponents associated with the ergodic measure with either full supportor positive entropy is an interval.

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页数：11

相关论文

共 25 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] NONUNIFORM HYPERBOLICITY FOR C1-GENERIC DIFFEOMORPHISMS [J].

Abdenur, Flavio ;

Bonatti, Christian ;

Crovisier, Sylvain .

ISRAEL JOURNAL OF MATHEMATICS, 2011, 183 (01) :1-60

[3] Robust Criterion for the Existence of Nonhyperbolic Ergodic Measures [J].

Bochi, Jairo ;

Bonatti, Christian ;

Diaz, Lorenzo J. .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2016, 344 (03) :751-795

[4]

Bonatti C, 2018, MOSC MATH J, V18, P15

[5] Non-hyperbolic ergodic measures with large support [J].

Bonatti, Christian ;

Diaz, Lorenzo J. ;

Gorodetski, Anton .

NONLINEARITY, 2010, 23 (03) :687-705

[6]

Brin M., 1974, Izv. Akad. Nauk SSSR Ser. Mat, P170

[7] Non-zero Lyapunov exponents and uniform hyperbolicity [J].

Cao, YL .

NONLINEARITY, 2003, 16 (04) :1473-1479

[8] Partial hyperbolicity and homoclinic tangencies [J].

Crovisier, Sylvain ;

Sambarino, Martin ;

Yang, Dawei .

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2015, 17 (01) :1-49

[9] UNIFORM HYPERBOLICITY ALONG PERIODIC ORBITS [J].

Fakhari, Abbas .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2013, 141 (09) :3107-3118

[10] CENTER LYAPUNOV EXPONENTS IN PARTIALLY HYPERBOLIC DYNAMICS [J].

Gogolev, Andrey ;

Tahzibi, Ali .

JOURNAL OF MODERN DYNAMICS, 2014, 8 (3-4) :549-576