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Home > Art, Film & Photography > Topological Dynamics: Topological Entropy, Topological Conjugacy, Conley Index Theory, Milnor-Thurston Kneading Theory, Gustav A. Hedlund
Topological Dynamics: Topological Entropy, Topological Conjugacy, Conley Index Theory, Milnor-Thurston Kneading Theory, Gustav A. Hedlund

Topological Dynamics: Topological Entropy, Topological Conjugacy, Conley Index Theory, Milnor-Thurston Kneading Theory, Gustav A. Hedlund


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About the Book

Chapters: Topological Entropy, Topological Conjugacy, Conley Index Theory, Milnor-thurston Kneading Theory, Gustav A. Hedlund. Source: Wikipedia. Pages: 24. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: In mathematics, the topological entropy of a topological dynamical system is a nonnegative real number that measures the complexity of the system. Topological entropy was first introduced in 1965 by Adler, Konheim and McAndrew. Their definition was modelled after the definition of the KolmogorovSinai, or metric, entropy. Later, Dinaburg and Rufus Bowen gave a different, equivalent definition reminiscent of the Hausdorff dimension. The second definition clarified the meaning of the topological entropy: for a system given by an iterated function, the topological entropy represents the exponential growth rate of the number of distinguishable orbits of the iterates. An important variational principle relates the notions of topological and measure-theoretic entropy. A topological dynamical system consists of a Hausdorff topological space X (usually assumed to be compact) and a continuous self-map f. Its topological entropy is a nonnegative real number that can be defined in various ways, which are known to be equivalent. Let X be a compact Hausdorff topological space. For any finite cover C of X, let H(C) be the logarithm (usually to base 2) of the smallest number of elements of C that cover X. For two covers C and D, let be their (minimal) common refinement, which consists of all the non-empty intersections of a set from C with a set from D, and similarly for multiple covers. For any continuous map f: X X, the following limit exists: Then the topological entropy of f, denoted h(f), is defined to be the supremum of H(C, f) over all possible finite covers C of X. The parts of C may be viewed a...More: http: //booksllc.net/?id=546397


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Product Details
  • ISBN-13: 9781158560127
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • Sub Title: Topological Entropy, Topological Conjugacy, Conley Index Theory, Milnor-Thurston Kneading Theory, Gustav A. Hedlund
  • Width: 229 mm
  • ISBN-10: 1158560125
  • Publisher Date: 15 Sep 2010
  • Binding: Paperback
  • Spine Width: 2 mm
  • Weight: 50 gr


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