Ergodic Measures with Multi-zero Lyapunov Exponents Inside Homoclinic Classes

Xiaodong Wang; Jinhua Zhang

doi:10.1007/s10884-019-09752-3

Ergodic Measures with Multi-zero Lyapunov Exponents Inside Homoclinic Classes

Xiaodong Wang
, Jinhua Zhang^*

^*Corresponding author for this work

Shanghai Jiao Tong University
Université Paris-Sud 11

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper, we prove that for C¹-generic diffeomorphisms, if a homoclinic class contains periodic orbits of indices i and j with j> i+ 1 , and the homoclinic class has no-domination of index l for any l∈ { i+ 1 , … , j- 1 } , then there exists a non-hyperbolic ergodic measure with more than one vanishing Lyapunov exponents and whose support is the whole homoclinic class. Some other results are also obtained.

Original language	English
Pages (from-to)	631-664
Number of pages	34
Journal	Journal of Dynamics and Differential Equations
Volume	32
Issue number	2
DOIs	https://doi.org/10.1007/s10884-019-09752-3
State	Published - 1 Jun 2020
Externally published	Yes

Keywords

Dominated splitting
Homoclinic class
Lyapunov exponent
Non-hyperbolic ergodic measure

Access to Document

10.1007/s10884-019-09752-3

Cite this

@article{865ae6bdab8547808b1100c5dce1dddb,

title = "Ergodic Measures with Multi-zero Lyapunov Exponents Inside Homoclinic Classes",

abstract = "In this paper, we prove that for C1-generic diffeomorphisms, if a homoclinic class contains periodic orbits of indices i and j with j> i+ 1 , and the homoclinic class has no-domination of index l for any l∈ \{ i+ 1 , … , j- 1 \} , then there exists a non-hyperbolic ergodic measure with more than one vanishing Lyapunov exponents and whose support is the whole homoclinic class. Some other results are also obtained.",

keywords = "Dominated splitting, Homoclinic class, Lyapunov exponent, Non-hyperbolic ergodic measure",

author = "Xiaodong Wang and Jinhua Zhang",

note = "Publisher Copyright: {\textcopyright} 2019, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2020",

month = jun,

day = "1",

doi = "10.1007/s10884-019-09752-3",

language = "英语",

volume = "32",

pages = "631--664",

journal = "Journal of Dynamics and Differential Equations",

issn = "1040-7294",

publisher = "Springer",

number = "2",

}

TY - JOUR

T1 - Ergodic Measures with Multi-zero Lyapunov Exponents Inside Homoclinic Classes

AU - Wang, Xiaodong

AU - Zhang, Jinhua

PY - 2020/6/1

Y1 - 2020/6/1

N2 - In this paper, we prove that for C1-generic diffeomorphisms, if a homoclinic class contains periodic orbits of indices i and j with j> i+ 1 , and the homoclinic class has no-domination of index l for any l∈ { i+ 1 , … , j- 1 } , then there exists a non-hyperbolic ergodic measure with more than one vanishing Lyapunov exponents and whose support is the whole homoclinic class. Some other results are also obtained.

AB - In this paper, we prove that for C1-generic diffeomorphisms, if a homoclinic class contains periodic orbits of indices i and j with j> i+ 1 , and the homoclinic class has no-domination of index l for any l∈ { i+ 1 , … , j- 1 } , then there exists a non-hyperbolic ergodic measure with more than one vanishing Lyapunov exponents and whose support is the whole homoclinic class. Some other results are also obtained.

KW - Dominated splitting

KW - Homoclinic class

KW - Lyapunov exponent

KW - Non-hyperbolic ergodic measure

UR - https://www.scopus.com/pages/publications/85064822021

U2 - 10.1007/s10884-019-09752-3

DO - 10.1007/s10884-019-09752-3

M3 - 文章

AN - SCOPUS:85064822021

SN - 1040-7294

VL - 32

SP - 631

EP - 664

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

IS - 2

ER -

Ergodic Measures with Multi-zero Lyapunov Exponents Inside Homoclinic Classes

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this