![]() ![]() Kupka, On turbulent, erratic and other dynamical properties of Zadeh's extensions, Chaos Solitons Fractals, 44 (November 2011) 990-994. An Introduction, Marcel Dekker, Inc., New York, 1992. Misiurewicz, Embedding inverse limits of interval maps as attractors, Fundam. Mardei, On covering dimension and inverse limits of compact spaces, Ill. Sternfeld, Hyperspaces of two-dimensional continua, Fundam. Kupka, On Devaney chaotic induced dynamical systems, Fuzzy Sets Syst., 177 (2011) 34-44. Kupka, On fuzzifications of discrete dynamical systems, Inf. ![]() ![]() Kloeden, Fuzzy dynamical systems, Fuzzy Sets Syst., 7 (1982) 275-296. Yorke, Inverse limits and an implicitly defined difference equation from economics, Topol. br0190 Boju Jiang, No embeddings of solenoids into surfaces, Proc.From Continua to Chaos, Springer, New York, 2012. Voxman, Topological properties of fuzzy numbers, Fuzzy Sets Syst., 10 (1983) 87-99. Freudenthal, Entwicklungen yon Rdumen und ihren Gruppen, Compos. Engelking, Zarys topologii oglnej (Polish), Pastwowe Wydawnictwo Naukowe, Warsaw, 1965. Dumitrescu, Entropy of fuzzy dynamical systems, Fuzzy Sets Syst., 70 (1995) 45-57. Diamond, Chaos in iterated fuzzy systems, J. Esterle, Michael's problem and the PoincarFatouBieberbach phenomenon, Bull. Cramer, Inverse limit reflection and the structure of L(V+1), J. Li, Dynamical connections between a continuous map and its inverse limit space, in: Lecture Notes in Pure and Appl. Kupka, On the topological entropy on the space of fuzzy numbers, Fuzzy Sets Syst., 257 (2014) 132-145. Bruin, Planar embeddings of inverse limit spaces of unimodal maps, Topol. Brown, Some applications of an approximation theorem for inverse limits, Proc. Brown, Inverse limits, entropy and weak isomorphism for discrete dynamical systems, Trans. Hall, New rotation sets in a family of torus homeomorphisms, Invent. Hall, Inverse limits as attractors in parameterized families, Bull. Diamond, The dynamics of continuous maps of finite graphs through inverse limits, Trans. Martin, The construction of global attractors, Proc. Martin, Chaos, periodicity, and snakelike continua, Trans. These ideas have considerable scope for further development, and a list of problems and lines of research is included. This leads to new, elegant concepts (defined purely topologically) of self-similarity and fractality: in particular, the author shows that many invariant sets are "visually fractal", i.e. The last and most original 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. 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 much more slickly than before. The first part of the book develops certain hyperspace theory concerning the Hausdorff metric and the Vietoris topology, as a foundation for what follows on self-similarity and fractality. 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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