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

This book is an elementary introduction to the theory of discrete dynamical systems, also stressing 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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Vries, Jan de (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin ; Boston : De Gruyter, [2014]
Colección:De Gruyter studies in mathematics.
Temas:
Topological dynamics.
Dynamique topologique.
MATHEMATICS > Calculus.
MATHEMATICS > Mathematical Analysis.
Topological dynamics
Topologische Dynamik
Almost periodic points and minimal sets.
Chaos.
Discrete dynamical systems.
Recurrence.
Shift systems and symbolic dynamics.
Symptotic stability and attraction.
Topological entropy.
Acceso en línea:Texto completo

MARC

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100 1 |a Vries, Jan de,  |e author. 
245 1 0 |a Topological Dynamical Systems :  |b an Introduction to the Dynamics of Continuous Mappings /  |c Jan de Vries. 
264 1 |a Berlin ;  |a Boston :  |b De Gruyter,  |c [2014] 
264 4 |c Ã2014 
300 |a 1 online resource (xv, 498 pages) :  |b illustrations. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a De Gruyter Studies in Mathematics ;  |v volume 59 
504 |a Includes bibliographical references (pages 481-484) and index. 
505 0 |a 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. 
505 8 |a 2.5 The Markov graph of a periodic orbit in an interval 2.6 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. 
505 8 |a 5.4 Factor maps 5.5 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. 
505 8 |a A Topology A.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. 
520 |a This book is an elementary introduction to the theory of discrete dynamical systems, also stressing 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. 
588 |a Description based on online resource; title from digital title page (viewed on January 26, 2024). 
546 |a English. 
590 |a eBooks on EBSCOhost  |b EBSCO eBook Subscription Academic Collection - Worldwide 
590 |a ProQuest Ebook Central  |b Ebook Central Academic Complete 
650 0 |a Topological dynamics. 
650 6 |a Dynamique topologique. 
650 7 |a MATHEMATICS  |x Calculus.  |2 bisacsh 
650 7 |a MATHEMATICS  |x Mathematical Analysis.  |2 bisacsh 
650 7 |a Topological dynamics  |2 fast 
650 7 |a Topologische Dynamik  |2 gnd 
653 |a Almost periodic points and minimal sets. 
653 |a Chaos. 
653 |a Discrete dynamical systems. 
653 |a Recurrence. 
653 |a Shift systems and symbolic dynamics. 
653 |a Symptotic stability and attraction. 
653 |a Topological entropy. 
758 |i has work:  |a Topological dynamical systems (Text)  |1 https://id.oclc.org/worldcat/entity/E39PCFt63KFcDPjVcVvQBQdDG3  |4 https://id.oclc.org/worldcat/ontology/hasWork 
776 0 8 |i Print version:  |a Vries, J. de (Jan).  |t Topological dynamical systems.  |d Berlin ; Boston : De Gruyter, [2014]  |z 9783110340730  |w (DLC) 2013041808  |w (OCoLC)881660419 
830 0 |a De Gruyter studies in mathematics. 
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