Hyperbolic Lyapunov-Perron regular points and smooth invariant measures

被引：0

作者：

ALANSARI, N. A. W. A. F. ^{[1
]}

机构：

[1] Penn State Univ, Dept Math, State Coll, PA 16801 USA

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2023年 / 43卷 / 07期

关键词：

Lyapunov-Perron regularity; smooth measures; SRB; hyperbolicity; entropy; SRB MEASURES; SYMBOLIC DYNAMICS; CENTRAL DIRECTION; METRIC ENTROPY; DIFFEOMORPHISMS; SYSTEMS;

D O I：

10.1017/etds.2022.31

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a C1+alpha diffeomorphism f of a compact smooth manifold, we give a necessary and sufficient condition that guarantees that if the set of hyperbolic Lyapunov-Perron regular points has positive volume, then f preserves a smooth measure. We use recent results on symbolic coding of chi-non-uniformly hyperbolic sets and results concerning the existence of SRB measures for them.

引用

页码：2177 / 2200

页数：24

共 14 条

[1] Absolute continuity of hyperbolic invariant measures for endomorphisms
Liu, Pei-Dong
Shu, Lin
NONLINEARITY, 2011, 24 (05) : 1595 - 1611
[2] Invariant manifolds near hyperbolic fixed points
Homburg, Ale Jan
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2006, 12 (10) : 1057 - 1068
[3] Invariant family of leaf measures and the Ledrappier-Young property for hyperbolic equilibrium states
Ben Ovadia, Snir
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2023, 43 (11) : 3603 - 3635
[4] INVARIANT MEASURES OF THE TOPOLOGICAL FLOW AND MEASURES AT INFINITY ON HYPERBOLIC GROUPS
Cantrell, Stephen
Tanaka, Ryokichi
JOURNAL OF MODERN DYNAMICS, 2024, 20 : 215 - 274
[5] Asymptotic measures for hyperbolic piecewise smooth mappings of a rectangle
Jakobson, M
Newhouse, S
ASTERISQUE, 2000, (261) : 103 - 159
[6] On the Smooth Dependence of SRB Measures for Partially Hyperbolic Systems
Zhang, Zhiyuan
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2018, 358 (01) : 45 - 79
[7] Natural invariant measures, divergence points and dimension in one-dimensional holomorphic dynamics
Ingle, William
Kaufmann, Jacie
Wolf, Christian
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2009, 29 : 1235 - 1255
[8] RETURN TIME STATISTICS OF INVARIANT MEASURES FOR INTERVAL MAPS WITH POSITIVE LYAPUNOV EXPONENT
Bruin, Henk
Todd, Mike
STOCHASTICS AND DYNAMICS, 2009, 9 (01) : 81 - 100
[9] On the Hausdorff dimension of invariant measures of piecewise smooth circle homeomorphisms
Trujillo, Frank
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2024, 44 (12) : 3599 - 3629
[10] Strictly hyperbolic equations with coefficients low-regular in time and smooth in space
Cicognani, Massimo
Lorenz, Daniel
JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, 2018, 9 (03) : 643 - 675

← 1 2 →