A shadowing lemma for quasi-hyperbolic strings of flows

Bo Han; Xiao Wen

doi:10.1016/j.jde.2017.08.065

A shadowing lemma for quasi-hyperbolic strings of flows

Bo Han
, Xiao Wen^*

^*Corresponding author for this work

School of Artificial Intelligence(Institute of Artificial Intelligence)

Beihang University

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

9 Scopus citations

Abstract

In this paper we prove a shadowing lemma for pseudo orbits made by quasi-hyperbolic strings. We allow singularities in question and hence, in particular, the quasi-hyperbolic strings are formulated by the rescaled linear Poincaré flow instead of the usual linear Poincaré flow. We also introduce the sectional Poincaré map and rescaled sectional Poincaré map for Lipschitz vector fields on Banach spaces in the article.

Original language	English
Pages (from-to)	1-29
Number of pages	29
Journal	Journal of Differential Equations
Volume	264
Issue number	1
DOIs	https://doi.org/10.1016/j.jde.2017.08.065
State	Published - 5 Jan 2018

Keywords

Dominated splitting
Linear Poincaré flow
Quasi-hyperbolic string
Sectional Poincaré map
Shadowing property

Access to Document

10.1016/j.jde.2017.08.065

Cite this

@article{394dba7610114d748320a0e16a25ce69,

title = "A shadowing lemma for quasi-hyperbolic strings of flows",

abstract = "In this paper we prove a shadowing lemma for pseudo orbits made by quasi-hyperbolic strings. We allow singularities in question and hence, in particular, the quasi-hyperbolic strings are formulated by the rescaled linear Poincar{\'e} flow instead of the usual linear Poincar{\'e} flow. We also introduce the sectional Poincar{\'e} map and rescaled sectional Poincar{\'e} map for Lipschitz vector fields on Banach spaces in the article.",

keywords = "Dominated splitting, Linear Poincar{\'e} flow, Quasi-hyperbolic string, Sectional Poincar{\'e} map, Shadowing property",

author = "Bo Han and Xiao Wen",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2018",

month = jan,

day = "5",

doi = "10.1016/j.jde.2017.08.065",

language = "英语",

volume = "264",

pages = "1--29",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - A shadowing lemma for quasi-hyperbolic strings of flows

AU - Han, Bo

AU - Wen, Xiao

PY - 2018/1/5

Y1 - 2018/1/5

N2 - In this paper we prove a shadowing lemma for pseudo orbits made by quasi-hyperbolic strings. We allow singularities in question and hence, in particular, the quasi-hyperbolic strings are formulated by the rescaled linear Poincaré flow instead of the usual linear Poincaré flow. We also introduce the sectional Poincaré map and rescaled sectional Poincaré map for Lipschitz vector fields on Banach spaces in the article.

AB - In this paper we prove a shadowing lemma for pseudo orbits made by quasi-hyperbolic strings. We allow singularities in question and hence, in particular, the quasi-hyperbolic strings are formulated by the rescaled linear Poincaré flow instead of the usual linear Poincaré flow. We also introduce the sectional Poincaré map and rescaled sectional Poincaré map for Lipschitz vector fields on Banach spaces in the article.

KW - Dominated splitting

KW - Linear Poincaré flow

KW - Quasi-hyperbolic string

KW - Sectional Poincaré map

KW - Shadowing property

UR - https://www.scopus.com/pages/publications/85029169442

U2 - 10.1016/j.jde.2017.08.065

DO - 10.1016/j.jde.2017.08.065

M3 - 文章

AN - SCOPUS:85029169442

SN - 0022-0396

VL - 264

SP - 1

EP - 29

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -

A shadowing lemma for quasi-hyperbolic strings of flows

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this