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SHADOWABLE CHAIN COMPONENTS AND HYPERBOLICITY
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 Title & Authors
SHADOWABLE CHAIN COMPONENTS AND HYPERBOLICITY
Lee, Manseob; Lee, Seunghee; Park, Junmi;
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 Abstract
We show that -generically, the shadowable chain component of a -vector field containing a hyperbolic periodic orbit is hyperbolic if it is locally maximal.
 Keywords
hyperbolic;shadowable;chain component;
 Language
English
 Cited by
 References
1.
A. Arbieto, L. Senos, and T. Sodero, The specification property for flows from the robust and generic viewpoint, J. Differential Equations 253 (2012), no. 1, 1893-1909. crossref(new window)

2.
C. Bonatti and S. Crovisier, Recurrence et genericite, Invent. Math. 158 (2004), no. 1, 33-104.

3.
C. Bonatti and L. Diaz, Robust heterodimensional cycles and $C^1$-generic dynamics, J. Inst. Math. Jussieu 7 (2008), no. 3, 469-525.

4.
S. Hayashi, Connecting invariant manifolds and the solution of the $C^1$ stability and ${\Omega}$-stability conjectures for flows, Ann. of Math. 145 (1997), no. 1, 81-137. crossref(new window)

5.
K. Lee, M. Lee, and S. Lee, Hyperbolicity of expansive homoclinic classes, preprint.

6.
K. Lee, L. Tien, and X. Wen, Robustly shadowable chain component of $C^1$-vector fields, J. Korean Math. Soc. 51 (2014), no. 1, 17-53. crossref(new window)

7.
K. Moriyasu, K. Sakai, and N. Sumi, Vector fields with topological stability, Trans. Amer. Math. Soc. 353 (2001), no. 8, 3391-3408. crossref(new window)

8.
R. Ribeiro, Hyperbolicity and types of shadowing for $C^1$ generic vector fields, arXiv: 1305.2977v1.

9.
K. Sakai, $C^1$-stably shadowable chain components, Ergodic Theory Dynam. Systems 28 (2008), no. 3, 987-1029.

10.
L. Senos, Generic Bowen-expansive flows, Bull. Braz. Math. Soc. 43 (2012), no. 1, 59-71. crossref(new window)

11.
L. Wen, S. Gan, and X. Wen, $C^1$-stably shadowable chain components are hyperbolic, J. Differential Equations 236 (2009), no. 1, 340-357.