E Book

Dynamical Systems

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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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Ketersediaan

Informasi Detail

Judul Seri

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No. Panggil

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Penerbit

Berlin, Heidelberg : Springer., 2005

Deskripsi Fisik

VIII, 190 p. 65 illus., 15 illus. in color.online resource.

Bahasa

English

ISBN/ISSN

9783540288893

Klasifikasi

530

Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

1st ed. 2005.

Subjek

Mathematics.
Operations research.
Decision making.
Operations Research/Decision Theory.
Physics.
Economic theory.
Economic Theory/Quantitative Economics/Mathematical Methods.
Dynamics.
Mathematics, general.
Physics, general.
Calculus of variations.
Calculus of Variations and Optimal Control; Optimization.
Ergodic theory.
Dynamical Systems and Ergodic Theory.

Info Detail Spesifik

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Pernyataan Tanggungjawab

Jürgen Jost.

Versi lain/terkait

Lampiran Berkas

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