Browse > Article
http://dx.doi.org/10.4134/CKMS.2012.27.3.613

LIMIT WEAK SHADOWABLE TRANSITIVE SETS OF C1-GENERIC DIFFEOMORPHISMS  

Lee, Man-Seob (Department of Mathematics Mokwon University)
Lu, Gang (Department of Mathematics, School of Science ShenYang University of Technology)
Publication Information
Communications of the Korean Mathematical Society / v.27, no.3, 2012 , pp. 613-619 More about this Journal
Abstract
In this paper, we prove that locally maximal transitive set of a $C^1$-generic diffeomorphism is hyperbolic if and only if it is limit weak shadowable.
Keywords
weak shadowing; limit weak shadowing; transitive set; hyperbolic; generic;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 R. Mane, An ergodic closing lemma, Ann. of Math. (2) 116 (1982), no. 3, 503-540.   DOI
2 S. Pilyugin, Shadowing in Dynamical Systems, Lecture Notes in Math., 1706, Springer 1999.
3 S. Pilyugin, K. Sakai, and O. Tarakanov, Transversality properties and $C^1$-open sets of diffeomorphisms with weak shadowing, Discrete Contin. Dyn. Syst. 16 (2006), no. 4, 871-882.   DOI
4 O. B. Plamenevskaya, Weak shadowing in two-dimensional diffeomorphisms, Vestnik St. Petersburg Univ. Math. 31 (1999), no. 3, 49-56.
5 K. Sakai, Diffeomorphisms with weak shadowing, Fund. Math. 168 (2001), no. 1, 57-75.   DOI
6 K. Sakai, A note on weak shadowing, Far East J. Dyn. Syst. 3 (2001), no. 1, 45-49.
7 K. Sakai, Diffeomorphisms with limit weak shadowing, Trends in Mathematics 7 (2004), 19-27.
8 D. Yang, Stably weakly shadowing transitive sets and dominated splittings, Proc. Amer. Math. Soc. 139 (2011), no. 8, 2747-2751.   DOI   ScienceOn
9 F. Abdenur and L. J. Diaz, Pseudo-orbit shadowing in the $C^1$ topology, Discrete Contin. Dyn. Syst. 17 (2007), no. 2, 223-245.
10 F. Abdenur, Generic robustness of spectral decompositions, Ann. Sci. Ecole Norm. Sup. (4) 36 (2003), no. 2, 213-224.   DOI
11 T. Eirola, O. Nevanlinna, and S. Pilyugin, Limit shadowing property, Numer. Funct. Anal. Optim. 18 (1997), no. 1-2, 75-92.   DOI   ScienceOn
12 K. Lee and M. Lee, Hyperbolic of $C^1$-stably expansive homoclinic classes, Discrete Contin. Dyn. Syst. 27 (2010), no. 3, 1133-1145.   DOI
13 K. Lee and X. Wen, Shadowable chain transitive sets of $C^1$-generic diffeomorphisms, to apear in Bull. Korean. Math. Soc.