[KSCI] Korea Science Citation Index Service

Lee, Man-Seob (Department of Mathematics, Mokwon University)

Publication Information

Abstract

In this paper, we show that if a transitive set ${\Lambda}$ is $C^1$ -stably expansive, then ${\Lambda}$ admits a dominated splitting.

Keywords

expansive; transitive set; dominated splitting; chain transitive set;

Citations & Related Records

1	K. Lee, G. Lu & X. Wen: $C^1$ -stably weak shadowing property of chain transitive sets. preprint.
2	K. Lee & M. Lee: Hyperbolicity of $C^1$ -stably expansive homoclinic classes. Disc. & Contin. Dynam. Syst. 27 (2010), 1133-1145. DOI
3	R. Mane: Expansive diffeomorphisms. Lecture Notes in Math. 468, Springer-Verlag (1975), 162-174.
4	R. Mane: An ergodic closing lemma. Ann. Math. 116 (1982), 503-540. DOI ScienceOn
5	D. Yang: Stably weakly shadowing transiteve sets and dominated splitting. Proc. Amer. Math. Soc. 139 (2011), 2747-2751. DOI ScienceOn
6	C. Bonatti, N. Gourmelon & T. Vivier: Perturbations of the derivative along periodic orbits. Ergodi. Th. & Dynm. Syst. 26 (2006), 1307-1337. DOI ScienceOn
7	N. Aoki & K. Hiraide: Topological Theory of Dynamical Systems. Recent Advances. North-Holland Math. Library 52 North-Holland, Amsterdam 1994.
8	C. Bonatti, L.J.Diaz & E. Pujals: A $C^1$ -generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks or sources. Annals of Math. 158 (2003), 187-222.