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LIMIT WEAK SHADOWABLE TRANSITIVE SETS OF C1-GENERIC DIFFEOMORPHISMS
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 Title & Authors
LIMIT WEAK SHADOWABLE TRANSITIVE SETS OF C1-GENERIC DIFFEOMORPHISMS
Lee, Man-Seob; Lu, Gang;
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 Abstract
In this paper, we prove that locally maximal transitive set of a -generic diffeomorphism is hyperbolic if and only if it is limit weak shadowable.
 Keywords
weak shadowing;limit weak shadowing;transitive set;hyperbolic;generic;
 Language
English
 Cited by
 References
1.
F. Abdenur, Generic robustness of spectral decompositions, Ann. Sci. Ecole Norm. Sup. (4) 36 (2003), no. 2, 213-224.

2.
F. Abdenur and L. J. Diaz, Pseudo-orbit shadowing in the $C^1$ topology, Discrete Contin. Dyn. Syst. 17 (2007), no. 2, 223-245.

3.
T. Eirola, O. Nevanlinna, and S. Pilyugin, Limit shadowing property, Numer. Funct. Anal. Optim. 18 (1997), no. 1-2, 75-92. crossref(new window)

4.
K. Lee and M. Lee, Hyperbolic of $C^1$-stably expansive homoclinic classes, Discrete Contin. Dyn. Syst. 27 (2010), no. 3, 1133-1145. crossref(new window)

5.
K. Lee and X. Wen, Shadowable chain transitive sets of $C^1$-generic diffeomorphisms, to apear in Bull. Korean. Math. Soc.

6.
R. Mane, An ergodic closing lemma, Ann. of Math. (2) 116 (1982), no. 3, 503-540. crossref(new window)

7.
S. Pilyugin, Shadowing in Dynamical Systems, Lecture Notes in Math., 1706, Springer 1999.

8.
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. crossref(new window)

9.
O. B. Plamenevskaya, Weak shadowing in two-dimensional diffeomorphisms, Vestnik St. Petersburg Univ. Math. 31 (1999), no. 3, 49-56.

10.
K. Sakai, Diffeomorphisms with weak shadowing, Fund. Math. 168 (2001), no. 1, 57-75. crossref(new window)

11.
K. Sakai, A note on weak shadowing, Far East J. Dyn. Syst. 3 (2001), no. 1, 45-49.

12.
K. Sakai, Diffeomorphisms with limit weak shadowing, Trends in Mathematics 7 (2004), 19-27.

13.
D. Yang, Stably weakly shadowing transitive sets and dominated splittings, Proc. Amer. Math. Soc. 139 (2011), no. 8, 2747-2751. crossref(new window)