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Chaotische Dynamische Systeme
Paperback
General MathematicsGeneral Science
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ISBN13: 9783662723883
Publisher: Springer Spektrum
Published: Apr 7 2026
Pages: 209
Language: German
In diesem Buch entwickeln wir die mathematische Theorie zeitdiskreter dynamischer Systeme. Unser Schwerpunkt liegt hierbei auf der Definition sowie der qualitativen und quantitativen Untersuchung chaotischer Systeme. Zu Beginn stellen wir Grundbegriffe der Theorie zeitdiskreter dynamischer Systeme vor und erläutern diese anhand von Beispielen. Im Folgenden gehen wir gängige Definitionen chaotischer Systeme an und diskutieren den Zusammenhang dieser Begriffe.
Mit der symbolischen Dynamik und der symbolischen Kodierung besprechen wir daraufhin den Kern der topologischen Theorie chaotischer dynamischer Systeme. Wir führen die symbolische Kodierung einiger paradigmatischer Systeme durch. Die ma theoretische Untersuchung chaotischer Systeme ist ein Teil der Ergodentheorie. Diese stellen wir kompakt vor und wenden sie auf eine Reihe von dynamischen Systemen an. Des Weiteren stellen wir numerische Methoden dar, die Indizien für eine chaotische Entwicklung eines dynamischen Systems bereitstellen können.
Im letzten Kapitel des Buches stellen wir eine Reihe von chaotischen Systemen vor, die aus den empirischen Wissenschaften stammen. Zusätzlich stellen wir in einem abschlie enden Kapitel den Zusammenhang zeitdiskreter und zeitkontinuierlicher dynamischer Systeme dar. Ein Anhang des Buches dient dem Nachschlagen der mathematischen Grundbegriffe, die wir verwenden.
Das Buch wendet sich an Studierende, die Grundkenntnisse der Analysis und Linearen Algebra haben, wie sie in entsprechenden Vorlesungen und Lehrbüchern vermittelt wird. Das Buch kann als Grundlage einer Vorlesung im letzten Jahr eines Bachelorstudiengangs oder einer Vorlesung in einem Master Studiengang in Mathematik, Physik oder Informatik verwendet werden.
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