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Topological Dynamical Systems : an Introduction to the Dynamics of Continuous Mappings.

Author: Jan Vries
Publisher: Berlin : De Gruyter, [2014] ©2014
Series: De Gruyter studies in mathematics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This bookis anelementary introduction to the theory of discrete dynamical systems, alsostressing the topological background of the topic. It treats all important concepts needed to understand recent literature from the 'applied general topology' angle. The book is addressed to graduate students and beyond.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jan Vries
ISBN: 3110342405 9783110342406
OCLC Number: 873464768
Language Note: In English.
Description: 1 online resource (xv, 498 pages) : illustrations.
Contents: Preface; Notation; 0 Introduction; 0.1 Definition and a (very brief) historical overview; 0.2 Continuous vs. discrete time; 0.3 The dynamical systems point of view; 0.4 Examples; 1 Basic notions; 1.1 Invariant and periodic points; 1.2 Invariant sets; 1.3 Transitivity; 1.4 Limit sets; 1.5 Topological conjugacy and factor mappings; 1.6 Equicontinuity and weak mixing; 1.7 Miscellaneous examples; 2 Dynamical systems on the real line; 2.1 Graphical iteration; 2.2 Existence of periodic orbits; 2.3 The truncated tent map; 2.4 The double of a mapping. 2.5 The Markov graph of a periodic orbit in an interval2.6 Transitivity of mappings of an interval; 3 Limit behaviour; 3.1 Limit sets and attraction; 3.2 Stability; 3.3 Stability and attraction for periodic orbits; 3.4 Asymptotic stability in locally compact spaces; 3.5 The structure of (asymptotically) stable sets; 4 Recurrent behaviour; 4.1 Recurrent points; 4.2 Almost periodic points and minimal orbit closures; 4.3 Non-wandering points; 4.4 Chain-recurrence; 4.5 Asymptotic stability and basic sets; 5 Shift systems; 5.1 Notation and terminology; 5.2 The shift mapping; 5.3 Shift spaces. 5.4 Factor maps5.5 Subshifts and graphs; 5.6 Recurrence, almost periodicity and mixing; 6 Symbolic representations; 6.1 Topological partitions; 6.2 Expansive systems; 6.3 Applications; 7 Erratic behaviour; 7.1 Stability revisited; 7.2 Chaos(1): sensitive systems; 7.3 Chaos(2): scrambled sets; 7.4 Horseshoes for interval maps; 7.5 Existence of a horseshoe; 8 Topological entropy; 8.1 The definition; 8.2 Independence of the metric; factor maps; 8.3 Maps on intervals and circles; 8.4 The definition with covers; 8.5 Miscellaneous results; 8.6 Positive entropy and horseshoes for interval maps. A TopologyA. 1 Elementary notions; A.2 Compactness; A.3 Continuous mappings; A.4 Convergence; A.5 Subspaces, products and quotients; A.6 Connectedness; A.7 Metric spaces; A.8 Baire category; A.9 Irreduciblemappings; A.10 Miscellaneous results; B The Cantor set; B.1 The construction; B.2 Proof of Brouwer's Theorem; B.3 Cantor spaces; C Hints to the Exercises; Literature; Index.
Series Title: De Gruyter studies in mathematics.
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Presents an introduction to the theory of discrete dynamical systems, also stressing the topological background of the topic.  Read more...

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