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Chain transitivity in hyperspaces
Chaos, Solitons & Fractals, 2015Given a non-empty compact metric space X and a continuous function f: X → X, we study the dynamics of the induced maps on the hyperspace of non-empty compact subsets of X and on various other invariant subspaces thereof, in particular symmetric products. We show how some important dynamical properties transfer across induced systems.
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Strong Chain Transitivity via Uniformity
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Chain transitivity and Lipschitz ergodicity
Nonlinear Analysis: Theory, Methods & Applications, 1998Let \(X\) be a compact metric space, \(f\) a homeomorphism of \(X\). The author studies concepts and improves results of \textit{R. Easton} [Lect. Notes Math. 668, 95-102 (1978; Zbl 0393.54027)]. It is shown that the induced action of \(f\) on an invariant subset \(A\) is Lipschitz-ergodic if and only \(A\) is \(E\)-chain transitive. If \(A\) is strong
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Chain transitivity and uniform persistence
Chaos, Solitons & Fractals, 2002Some results of \textit{M. W. Hirsch}, \textit{H. L. Smith} and \textit{X.-Q. Zhao} [J. Dyn. Differ. Equations 13, 107--131 (2001; Zbl 1129.37306)] on the uniform persistence for continuous maps on metric spaces are improved. Other properties of these maps (attractivity, strong repellers) are also addressed along the lines of the cited paper of Hirsch ...
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