A new criterion of physical measures for partially hyperbolic diffeomorphisms

Hua，Yongxia1; Yang，Fan2; Yang，Jiagang3,4

2020

10.1090/tran/7920

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY   影响因子和分区

0002-9947

1088-6850

We show that, for any C1 partially hyperbolic diffeomorphism, there is a full volume subset such that any Ces`aro limit of any point in this subset satisfies the Pesin formula for partial entropy. This result has several important applications. First, we show that, for any C1+ partially hyperbolic diffeomorphism with one dimensional center, there is a full volume subset such that either every point in this set belongs to the basin of a physical measure with nonvanishing center exponent or the center exponent of any limit of the sequence 1 nΣn-1 i=0 δfi(x) is vanishing. We also prove that, for any diffeomorphism with mostly contracting center, it admits a C1-neighborhood such that every diffeomorphism in a C1 residual subset of this open set admits finitely many physical measures whose basins have full volume.

SCI

英语

第一

NSFC[11401133]

Mathematics

Mathematics

WOS:000514306000013

AMER MATHEMATICAL SOC

MATHEMATICS

2-s2.0-85077562506

Scopus

1.Department of Mathematics,Southern University of Science and Technology of China,Xili, Nanshan District, Shenzhen, Guangdong,1088 Xueyuan Road,518055,China
2.Department of Mathematics,University of Oklahoma,Norman,73019,United States
3.Departamento de Geometria,Instituto de Matemática e Estatistica,Universidade Federal Fluminense,Niterói,Brazil
4.Department of Mathematics,Southern University of Science and Technology of China,Guangdong,China

Hua，Yongxia,Yang，Fan,Yang，Jiagang. A new criterion of physical measures for partially hyperbolic diffeomorphisms[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,2020,373(1):385-417.

Hua，Yongxia,Yang，Fan,&Yang，Jiagang.(2020).A new criterion of physical measures for partially hyperbolic diffeomorphisms.TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,373(1),385-417.

Hua，Yongxia,et al."A new criterion of physical measures for partially hyperbolic diffeomorphisms".TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 373.1(2020):385-417.