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http://dx.doi.org/10.14403/jcms.2019.32.2.165

DECOMPOSITION PROPERTY FOR C1 GENERIC DIFFEOMORPHISMS  

Lee, Manseob (Department of Mathematics, Mokwon University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.32, no.2, 2019 , pp. 165-170 More about this Journal
Abstract
$C^1$ generically, if a diffeomorphism $f:M{\rightarrow}M$ of a closed smooth Riemannian manifold M has the asymptotic average shadowing property or the average shadowing property then f has a decomposition property.
Keywords
shadowing; average shadowing; asymptotic average shadowing; dominated splitting; decomposition property;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 F. Abdenur, C. Bonatti, and S. Crovisier, Global dominated splittings and the $C^1$ Newhouse phenomenon, Proc. Amer. Math. Soc., 134 (2006), 2229-2237.   DOI
2 N. Aoki, On homeomorphisms with pseudo-orbit tracing property, Tokyo. J. Math. 6 (1983), 329-334.   DOI
3 M. L. Blank, Metric properties of $\epsilon$-trajectories of dynamical systems with stochastic behaviour, Ergod. Th. Dynam. Syst. 8 (1988), 365-378.   DOI
4 C. Bonatti and S. Crovisier, Recurrence and genericity, Invent. Math. 158 (2004), 33-104.   DOI
5 R. Gu, The asymptotic average shadowing property and transitivity, Nonlear Anal. 67 (2007), 1680-1689.   DOI
6 B. Honary and A. Z. Bahabadi, Asymptotic average shadowing property on compact metric spaces, Nonlinear Anal. 69 (2008), 2857-2863.   DOI
7 M. Lee, Diffeomorphisms with the stably asymptotic average shadowing property, J. Chungcheong Math. Soc. 23 (2010), 617-623.
8 M. Lee, Stably average shadowing property on homoclinic classes, Nonlinear Anal. 74 (2011), 689-694.   DOI
9 M. Lee, Average shadowing property on closed sets, Far East J. Math. Sci. 57 (2011), 171-179.
10 M. Lee, Chain transitive set with asymptotic average shadowing proeprty, Far East J. Math. Sci. 61 (2012), 207-212.
11 M. Lee, Asymptotic average shadowing in linear dynamical systems, Far East J. Math. Sci. 66 (2012), 37-44.
12 M. Lee, Stably asymptotic average shadowing property and dominated splitting, Advan. Differ, Equat. 25 (2012), 1-6.
13 M. Lee, Quasi-Anosov diffeomorphisms and various shadowing properties, J. Chungcheong Math. Soc. 29 (2016), 651-655.   DOI
14 M. Lee, Robustly chain transitive diffeomorpshisms, J. Ineqaul. Appl. 230 (2015), 6 pages.
15 M. Lee, A type of the shadowing properties for generic view points, Axioms, 7 (2018), 1-7.   DOI
16 M. Lee and J. Park, Asymptotic average shadowing property on a closed set, J. Chungcheong Math. Soc. 25 (2012), 27-33.   DOI
17 M. Lee and J. Park, Diffeomorphisms with average and asymptotic average shadowing, Dyn. Contin. Discrete Impuls. Syst. Ser. A. 23 (2016), 285-294.
18 M. Lee and X. Wen. Diffeomorphisms with $C^1$-stably average shadowing, Acta Math. Sin. Engl. Ser. 29 (2013), 85-92.   DOI
19 J. Park and Z. Yong, Average shadowing property on compact metric spaces, Commun. Korean Math. Soc. 21 (2006), 355-361.   DOI
20 K. Sakai, Diffeomorphisms with the average-shadowing property on two-dimensional closed manifolds, Rocky Mount. J. Math. 30 (2000), 425-437.   DOI
21 S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817.   DOI