[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2003.40.4.703

INVERSE SHADOWING FOR EXPANSIVE FLOWS

Lee, Keon-Hee (Department of Mathematics, Chungnam National University)
Lee, Zoon-Hee (Department of Mathematics, Chungnam National University)

Publication Information

Bulletin of the Korean Mathematical Society / v.40, no.4, 2003 , pp. 703-713 More about this Journal

Abstract

We extend the notion of inverse shadowing defined for diffeomorphisms to flows, and show that an expansive flow on a compact manifold with the shadowing property has the inverse shadowing property with respect to the classes of continuous methods. As a corollary we obtain that a hyperbolic flow also has the inverse shadowing property with respect to the classes of continuous methods.

Keywords

flow; expansive; method; shadowing; inverse shadowing;

Citations & Related Records

Reference

1	Hyperbolic homeomorphisms and bishadowing / [ P.Kloeden;J.Ombach ] / Ann. Polon Math. DOI
2	Continuous and inverse shadowing / [ P.Kloeden;J.Ombach;A.Pokrovskii ] / Functional Differential Equations
3	Inverse shadowing by continuous methods / [ S.Pilyugin ] / Discrete and Continuous Dynamical Systems DOI
4	Bishadowing and hyperbolicity / [ P.Diamond;Y.Han;K.Lee ] / International J. of Bifurcation and Chaos DOI ScienceOn
5	Expansive one-parameter flows / [ R.Bowen;P.Walters ] / J. Differential Equations DOI
6	Approximate and real trajectories for generic dynamical systems / [ R.Corless;S.Pilyugin ] / J. Math. Anal. Appl. DOI ScienceOn
7	Sinks, sources and saddles for expansive flows with the pseudo orbit tracing property / [ J.Ombach ] / Ann. Pol. Math.
8	Cannonical coordinates and the pseudo orbit tracing property / [ R.Thomas ] / J. Differential Equations DOI
9	Continuous inverse shadowing and hyperbolicity / [ K.Lee ] / Bull. Austral. Math. Soc. DOI
10	Stability properties of one-parameter flows / [ R.Thomas ] / Proc. London Math. Soc. DOI
11	Shadowing in structurally stable flows / [ S.Pilyugin ] / J. Differential Equations DOI ScienceOn
12	Shadowing in dynamical systms / [ S.Pilyugin ] / Lecture Notes in Math.

1	Dmitry Todorov. (2014) Dynamical Systems Lipschitz inverse shadowing for non-singular flows / 29 (1) , 40
4	Yinghao Han. (2004) Dynamical Systems Inverse shadowing for structurally stable flows / 19 (4) , 371
1	Keonhee Lee. (2013) Advances in Difference Equations Divergence-free vector fields with inverse shadowing / 2013 (1)