Titlebook: Topological Dimension and Dynamical Systems; Michel Coornaert Textbook 2015 Springer International Publishing Switzerland 2015 Amenable Gr

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Mean Topological Dimension for Continuous MapsIn this chapter, the term “dynamical system” refers to a pair (.), where . is a topological space and . a continuous map from . into itself.

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Shifts and Subshifts over ,In this chapter, we introduce the shift map . on the space of bi-infinite sequences of points in a topological space ..

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Applications of Mean Dimension to Embedding ProblemsIn this chapter, we prove the embedding theorem of Jaworski (Theorem .) which asserts that every dynamical system (., .), where . is a homeomorphism without periodic points of a compact metrizable space . such that ., embeds in the shift ..

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Amenable GroupsThis chapter is devoted to the class of amenable groups, a class of groups which contains all finite groups and all abelian groups and which is closed under several group operations, in particular taking subgroups, taking extensions, and taking direct limits.

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Textbook 2015ant of dynamical systems introduced in 1999 by Misha Gromov. The book examines how this invariant was successfully used by Elon Lindenstrauss and Benjamin Weiss to answer a long-standing open question about embeddings of minimal dynamical systems into shifts..A large number of revisions and addition

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instance the structure of atomic clusters and the marriage of density functional theory with molecular dynamics and simulated annealing, have provided additiona978-1-4757-9977-4978-1-4757-9975-0Series ISSN 0258-1221

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