![]() We also show the implications our results have for dynamics on continua. From our main theorem we derive an ε-chain version of Furstenberg's celebrated 2 implies n Theorem. Saved in: Bibliographic Details Author / Creator. from publication: Micro and Macro Fractals generated by multi-valued dynamical systems Given a multi-valued. ![]() These amongst others include, chain transitivity, chain (weakly) mixing, chain recurrence, exactness by chains. Download scientific diagram The dual fractal to the Koch Curve. ![]() We show how some important dynamical properties transfer across induced systems. Topological entropy of multivalued maps in topological spaces and hyperspaces. We also show the implications our results have for dynamics on continua.ĪB - Given 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. Solitons & Fractals 138(2):109898, 1-8, 2020, (ii) to generalize the. From our main theorem we derive an ε-chain version of Furstenberg's celebrated 2 implies n Theorem. These amongst others include, chain transitivity, chain (weakly) mixing, chain recurrence, exactness by chains. These ideas have considerable scope for further development, and a list of problems and lines of research is included.N2 - Given 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. This leads to concepts (defined purely topologically) of self-similarity and fractality: in particular, the author shows that many invariant sets are "visually fractal" - have infinite detail in a certain sense. The last part of the book introduces the notion of a "view" as part of a framework for studying the structure of sets within a given space. Addressed to all readers with an interest in fractals, hyperspaces, fixed-point theory, tilings and nonstandard analysis, this book presents its subject in an original and accessible way complete with many figures. ![]() Hutchinson's invariant sets (sets composed of smaller images of themselves) is developed, with a study of when such a set is tiled by its images and a classification of many invariant sets as either regular or residual. A major feature is that nonstandard analysis is used to obtain new proofs of some known results. The first part of the book develops certain hyperspace theories concerning the Hausdorff metric and the Vietoris topology, as a foundation for what follows on self-similarity and fractality. Li, The large deviations theorem and ergodic sensitivity. The first part of the book develops certain hyperspace theory concerning the Hausdorff metric and the Vietoris topology, as a. Addressed to all readers with an interest in fractals, hyperspaces, fixed-point theory, tilings and nonstandard analysis, this book presents its subject in an accessible way, complete with many figures. Li, A note on uniform convergence and transitivity, Chaos Solitons Fractals 45 (2012) 759764. Addressed to all readers with an interest in fractals, hyperspaces, fixed-point theory, tilings and nonstandard analysis, this book presents its subject in an original and accessible way complete with many figures. ![]()
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