Dynamical Systems [electronic resource] : Examples of Complex Behaviour / by Jürgen Jost.
By: Jost, Jürgen [author.].
Contributor(s): SpringerLink (Online service).
Material type: TextSeries: Universitext: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005Description: VIII, 190 p. 65 illus., 15 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540288893.Subject(s): Physics  Mathematics  Differentiable dynamical systems  Operations research  Economic theory  Mathematical optimization  Physics, general  Mathematics, general  Dynamical Systems and Ergodic Theory  Operations Research/Decision Theory  Economic Theory/Quantitative Economics/Mathematical Methods  Calculus of Variations and Optimal Control; OptimizationAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 530 Online resources: Click here to access onlineItem type  Current location  Call number  Status  Date due  Barcode  Item holds  

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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.
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.
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Dynamical systems by Jost Jurgen 
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