Stably inverse shadowable transitive sets and dominated splitting
Authors:
Keonhee Lee and Manseob Lee
Journal:
Proc. Amer. Math. Soc. 140 (2012), 217-226
MSC (2000):
Primary 37D30; Secondary 37C50
DOI:
https://doi.org/10.1090/S0002-9939-2011-10882-7
Published electronically:
May 19, 2011
MathSciNet review:
2833534
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Let 
be a diffeomorphism of a closed 
-dimensional smooth manifold. In this paper, we show that if 
has the 
-stably inverse shadowing property on a transitive set, then it admits a dominated splitting.
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-stability and structural satbility via inverse shadowing, Bull. Austral. Math. Soc. 74 (2006), 185-196. 
satisfy Axiom A, Ergod. Th. & Dynam. Syst. 12 (1992), 233-253. 
-stably inverse shadowing chain components for generic diffeomorphisms, Commun. Korean Math. Soc. 24 (2009), 127-144. Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 37D30, 37C50
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Additional Information
Keonhee Lee
Affiliation:
Department of Mathematics, Chungnam National University, Daejeon, 305-764, Republic of Korea
Email:
khlee@cnu.ac.kr
Manseob Lee
Affiliation:
Department of Mathematics, Mokwon University, Daejeon, 302-729, Republic of Korea
Email:
lmsds@mokwon.ac.kr
DOI:
https://doi.org/10.1090/S0002-9939-2011-10882-7
Keywords:
Dominated splitting,
genericity,
inverse shadowing,
transitive set.
Received by editor(s):
June 15, 2010
Received by editor(s) in revised form:
October 7, 2010, and November 3, 2010
Published electronically:
May 19, 2011
Additional Notes:
The second author is the corresponding author.
Communicated by:
Yingfei Yi
Article copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.