Dynamical Systems

Examples of Complex Behaviour
2005
ISBN: 978-3-540-22908-7
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 190 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 355 g

Reihe: Universitext

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.

Zielgruppe

Research

Autoren/Hrsg.

Jost, Jürgen

Fachgebiete

• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Wirtschaftstheorie, Wirtschaftsphilosophie
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Naturwissenschaften Physik Physik Allgemein Geschichte der Physik
• Mathematik | Informatik EDV | Informatik Informatik
• Naturwissenschaften Physik Physik Allgemein Experimentalphysik
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik

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.

Über Autor(innen)

Jürgen Jost is a widely-known and successful textbook author. His textbooks with Springer see related literature.