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Cover: 9783540229087 | Dynamical Systems | Examples of Complex Behaviour | Jürgen Jost | Buch
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Dynamical Systems
Examples of Complex Behaviour
Taschenbuch von Jürgen Jost
Sprache: Englisch

51,95 €*

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Lieferzeit 4-7 Werktage

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Beschreibung
Our aim is to introduce, explain, and discuss the fundamental problems, ideas, concepts, results, and methods of the theory of dynamical systems and to show how they can be used in speci?c examples. We do not intend to give a comprehensive overview of the present state of research in the theory of dynamical systems, nor a detailed historical account of its development. We try to explain the important results, often neglecting technical re?nements 1 and, usually, we do not provide proofs. One of the basic questions in studying dynamical systems, i.e. systems that evolve in time, is the construction of invariants that allow us to classify qualitative types of dynamical evolution, to distinguish between qualitatively di?erent dynamics, and to studytransitions between di?erent types. Itis also important to ?nd out when a certain dynamic behavior is stable under small perturbations, as well as to understand the various scenarios of instability. Finally, an essential aspect of a dynamic evolution is the transformation of some given initial state into some ?nal or asymptotic state as time proceeds. Thetemporalevolutionofadynamicalsystemmaybecontinuousordiscrete, butitturnsoutthatmanyoftheconceptstobeintroducedareusefulineither case.
Our aim is to introduce, explain, and discuss the fundamental problems, ideas, concepts, results, and methods of the theory of dynamical systems and to show how they can be used in speci?c examples. We do not intend to give a comprehensive overview of the present state of research in the theory of dynamical systems, nor a detailed historical account of its development. We try to explain the important results, often neglecting technical re?nements 1 and, usually, we do not provide proofs. One of the basic questions in studying dynamical systems, i.e. systems that evolve in time, is the construction of invariants that allow us to classify qualitative types of dynamical evolution, to distinguish between qualitatively di?erent dynamics, and to studytransitions between di?erent types. Itis also important to ?nd out when a certain dynamic behavior is stable under small perturbations, as well as to understand the various scenarios of instability. Finally, an essential aspect of a dynamic evolution is the transformation of some given initial state into some ?nal or asymptotic state as time proceeds. Thetemporalevolutionofadynamicalsystemmaybecontinuousordiscrete, butitturnsoutthatmanyoftheconceptstobeintroducedareusefulineither case.
Über den Autor
Jürgen Jost is a widely-known and successful textbook author. His textbooks with Springer see related literature.
Zusammenfassung

This book presents a survey of the field of dynamical systems and its significance for research in complex systems and other fields, based on a careful analysis of specific important examples. It also explains the fundamental underlying mathematical concepts, with a particular focus on invariants of dynamical systems, including a systematic treatment of Morse-Conley theory. Entropy and related concepts in the topological, metric, measure theoretic and smooth settings and some connections with information theory are discussed, and cellular automata and random Boolean networks are presented as specific examples.

Inhaltsverzeichnis
Stability of dynamical systems, bifurcations, and generic properties.- Discrete invariants of dynamical systems.- Entropy and topological aspects of dynamical systems.- Entropy and metric aspects of dynamical systems.- Entropy and measure theoretic aspects of dynamical systems.- Smooth dynamical systems.- Cellular automata and Boolean networks as examples of discrete dynamical systems.
Details
Erscheinungsjahr: 2005
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 204
Reihe: Universitext
Inhalt: viii
190 S.
50 s/w Illustr.
15 farbige Illustr.
190 p. 65 illus.
15 illus. in color.
ISBN-13: 9783540229087
ISBN-10: 3540229086
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Jost, Jürgen
Auflage: 2005
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Universitext
Maße: 235 x 155 x 13 mm
Von/Mit: Jürgen Jost
Erscheinungsdatum: 01.08.2005
Gewicht: 0,355 kg
preigu-id: 102227007
Über den Autor
Jürgen Jost is a widely-known and successful textbook author. His textbooks with Springer see related literature.
Zusammenfassung

This book presents a survey of the field of dynamical systems and its significance for research in complex systems and other fields, based on a careful analysis of specific important examples. It also explains the fundamental underlying mathematical concepts, with a particular focus on invariants of dynamical systems, including a systematic treatment of Morse-Conley theory. Entropy and related concepts in the topological, metric, measure theoretic and smooth settings and some connections with information theory are discussed, and cellular automata and random Boolean networks are presented as specific examples.

Inhaltsverzeichnis
Stability of dynamical systems, bifurcations, and generic properties.- Discrete invariants of dynamical systems.- Entropy and topological aspects of dynamical systems.- Entropy and metric aspects of dynamical systems.- Entropy and measure theoretic aspects of dynamical systems.- Smooth dynamical systems.- Cellular automata and Boolean networks as examples of discrete dynamical systems.
Details
Erscheinungsjahr: 2005
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 204
Reihe: Universitext
Inhalt: viii
190 S.
50 s/w Illustr.
15 farbige Illustr.
190 p. 65 illus.
15 illus. in color.
ISBN-13: 9783540229087
ISBN-10: 3540229086
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Jost, Jürgen
Auflage: 2005
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Universitext
Maße: 235 x 155 x 13 mm
Von/Mit: Jürgen Jost
Erscheinungsdatum: 01.08.2005
Gewicht: 0,355 kg
preigu-id: 102227007
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