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http://dx.doi.org/10.4134/CKMS.2006.21.3.515

VARIOUS INVERSE SHADOWING IN LINEAR DYNAMICAL SYSTEMS  

Choi, Tae-Young (Department of Mathematics Chungnam National University)
Lee, Keon-Hee (Department of Mathematics Chungnam National University)
Publication Information
Communications of the Korean Mathematical Society / v.21, no.3, 2006 , pp. 515-526 More about this Journal
Abstract
In this paper, we give a characterization of hyperbolic linear dynamical systems via the notions of various inverse shadowing. More precisely it is proved that for a linear dynamical system f(x)=Ax of ${\mathbb{C}^n}$, f has the ${\tau}_h$ inverse(${\tau}_h-orbital$ inverse or ${\tau}_h-weak$ inverse) shadowing property if and only if the matrix A is hyperbolic.
Keywords
inverse shadowing; weak inverse shadowing; orbital inverse shadowing; hyperbolicity;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 P. Kloeden, J. Ombach and A. Porkrovskii, Continuous and inverse shadowing, Funct. Diff. Equ. 6 (1999), 137-153
2 J. Lewowicz, Persistence in expansive systems, Ergodic Theory Dynam. Systems 3 (1983), 567-578
3 P. Diamond, K. Lee and Y. Han, Bishadowing and hyperbolicity, International Journal of Bifurcations and Chaos 12 (2002), 1779-1788   DOI   ScienceOn
4 P. Kloeden and J. Ombach, Hyperbolic homeomorphisms and bishadowing, Ann. Pol. Math 45, (1997), 171-177
5 T. Choi, S. Kim and K. Lee, Weak inverse shadowing and genericity, Bull. Korean Math. Soc. 43 (2006), 43-52   과학기술학회마을   DOI   ScienceOn
6 K. Lee, Continuous inverse shadowing and hyperbolicity, Bull. Austral. Math. Soc. 67 (2003), 15-26   DOI
7 S. Pilyugin, Shadowing in dynamical systems, Lecture Notes in Math. 1706, Springer-Verlag, Berlin, 1999, 182-185
8 S. Pilyugin, A. Rodionova and K. Sakai, Orbital and weak shadowing properties, Discrete and Continuous Dynamical Systems 9 (2003), 287-308   DOI
9 O. B. Plamenevskaya, Weak shadowing for two-dimensional diffeomorphisms, Vestnik St. Petersburg Univ. Math. 31 (1998), 49-56
10 R. Corless and S. Pilyugin, Approximate and real trajectories for generic dynamical systems, J. Math. Anal. Appl. 189 (1995), 409-423   DOI   ScienceOn
11 K. Lee and J. Park, Inverse shadowing of circle maps, Bull. Austral. Math. Soc. 69 (2004), 353-359   DOI
12 S. Pilyugin, Inverse shadowing by continuous methods, Discrete and Continuous Dynamical Systems 8 (2002), 29-38   DOI