On strong exponential limit shadowing property
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In this study, we show that the strong exponential limit shadowing property (SELmSP, for short), which has been recently introduced, exists on a neighborhood of a hyperbolic set of a diffeomorphism. We also prove that $\Omega$-stable diffeomorphisms and $\mathcal{\mathcal{L}}$-hyperbolic homeomorphisms have this type of shadowing property. By giving examples, it is shown that this type of shadowing is different from the other shadowings, and the chain transitivity and chain mixing are not necessary for it. Furthermore, we extend this type of shadowing property to positively expansive maps with the shadowing property.
Abstract
In this study, we show that the strong exponential limit shadowing property (SELmSP, for short), which has been recently introduced, exists on a neighborhood of a hyperbolic set of a diffeomorphism. We also prove that $\Omega$-stable diffeomorphisms and $\mathcal{\mathcal{L}}$-hyperbolic homeomorphisms have this type of shadowing property. By giving examples, it is shown that this type of shadowing is different from the other shadowings, and the chain transitivity and chain mixing are not necessary for it. Furthermore, we extend this type of shadowing property to positively expansive maps with the shadowing property.
참고문헌 (14)
- S. A. Ahmadi, "Exponential limit shadowing", Annales Polonici Mathematici, 108(1), pp.1~10 (2013), Institute of Mathematics, Polish Academy of Sciences[DOI]
- Ethan Akin, "Dynamics of topologically generic homeomorphisms", Memoirs of the American Mathematical Society, 164(783), pp.viii+130~ (2003), American Mathematical Society (AMS)[DOI]
- Bernardo Carvalho, "On homeomorphisms with the two-sided limit shadowing property", Journal of Mathematical Analysis and Applications, 420(1), pp.801~813 (2014), Elsevier BV[DOI]
- Timeo Eirola, "Limit shadowing property", Numerical Functional Analysis and Optimization, 18(1-2), pp.75~92 (1997), Informa UK Limited[DOI]
- Rongbao Gu, "The asymptotic average shadowing property and transitivity", Nonlinear Analysis: Theory, Methods & Applications, 67(6), pp.1680~1689 (2007), Elsevier BV[DOI]
- Marcin Kulczycki, "On almost specification and average shadowing properties", Fundamenta Mathematicae, 224(3), pp.241~278 (2014), Institute of Mathematics, Polish Academy of Sciences[DOI]
- Keonhee Lee, "Various shadowing properties and their equivalence", Discrete & Continuous Dynamical Systems - A, 13(2), pp.533~540 (2005), American Institute of Mathematical Sciences (AIMS)[DOI]
- K. Palmer, "Shadowing in dynamical systems" (2000), Kluwer Academic Publishers
- S. Yu. Pilyugin, "Shadowing in dynamical systems" (1999), Springer-Verlag
- Sergei Yu. Pilyugin, "Sets of Dynamical Systems with Various Limit Shadowing Properties", Journal of Dynamics and Differential Equations, 19(3), pp.747~775 (2007), Springer Science and Business Media LLC[DOI]
- Sergei Yu Pilyugin, "Lipschitz shadowing implies structural stability", Nonlinearity, 23(10), pp.2509~2515 (2010), IOP Publishing[DOI]
- O. B. Plamenevskaya, "Weak shadowing for two-dimensional dieomorphisms", Mat. Za-metki, 65, pp.477~480 (1999)
- Kazuhiro Sakai, "Shadowing properties of L-hyperbolic homeomorphisms", Topology and its Applications, 112(3), pp.229~243 (2001), Elsevier BV[DOI]
- Kazuhiro Sakai, "Various shadowing properties for positively expansive maps", Topology and its Applications, 131(1), pp.15~31 (2003), Elsevier BV[DOI]