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Einfhrung in die Analysis dynamischer Systeme

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Springer Nature
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N/A
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9783540207139
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Product Description

Dynamische Systeme stellen einen unverzichtbaren Bestandteil mathematischer Modellbildung fr Anwendungen aller Art dar, angefangen von Physik ber Biologie bis hin zur Informatik. Dieser Band fhrt in diese Theorie ein und beschreibt Methoden und Dynamiken, wie sie fr eine systematische Modellbildung auch in den Anwendungen notwendig erscheinen. Wesentliche Grundzge der Theorie werden beispielhaft im ersten Kapitel erlutert. Es schliet sich eine Einfhrung in niedrig-dimensionale Dynamiken an (u.a. rationale Funktionen), gefolgt von topologischer Dynamik (z.B. Attraktoren, Entropie und chaotisches Verhalten), differenzierbarer Dynamik (z.B. Liapunoff-Exponenten, Strukturstabilitt und Hyperbolizitt), Ergodentheorie (z.B. Ergodenstze, invariante Mae, Konservativitt) und schlielich thermodynamischer Formalismus (z.B. Gibbs-Theorie, Zetafunktionen).

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