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In this paper we deal with some shadowing properties of discrete dynamical systems on a compact metric space via the density of subdynamical systems. Let $f : X \to X$ be a continuous map of a compact metric space $X$ and $A$ be an $f$-invariant dense subspace of $X$. We show that if $f|_A:A\to A$ has the periodic shadowing property, then $f$ has the periodic shadowing property. Also, we show that $f$ has the finite average shadowing property if and only if $f|_A$ has the finite average shadowing property.
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참고문헌 (21)
참고문헌 신청
D. V. Anosov / 1970 / On a class of invariant sets of smooth dynamical systems / Proc. 5th Int. Conf. Nonl. Oscill 2:39~45
N. Aoki / 1994 / Topological Theory of Dynamical Systems / North-Holland Publishing Co
M. Baloush / 2016 / The dynamics of 1-step shifts of nite type over two symbols / Indian J. Sci. Tech 9(46):1~6
Andrew D. Barwell / 2013 / Characterizations of ω-limit sets in topologically hyperbolic systems / Discrete & Continuous Dynamical Systems - A 33(5):1819~1833
George D. Birkhoff / 1926 / An extension of Poincaré's last geometric theorem / Acta Mathematica 47(4):297~311
N. Aoki / 1994 / Topological Theory of Dynamical Systems / North-Holland Publishing Co
M. Baloush / 2016 / The dynamics of 1-step shifts of nite type over two symbols / Indian J. Sci. Tech 9(46):1~6
Andrew D. Barwell / 2013 / Characterizations of ω-limit sets in topologically hyperbolic systems / Discrete & Continuous Dynamical Systems - A 33(5):1819~1833
George D. Birkhoff / 1926 / An extension of Poincaré's last geometric theorem / Acta Mathematica 47(4):297~311
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