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2022 | OriginalPaper | Chapter

2. Deterministic Dynamical Systems

Author: Peter Müller

Published in: Handbook of Dynamics and Probability

Publisher: Springer International Publishing

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Abstract

In this chapter, we first give the general and abstract definition of a deterministic dynamical system. This definition has as its basic ingredients a state space whose points characterize the state of the system and a family of maps that determines the time evolution of states according to a dynamical law. The state space is comprised of the minimal set of variables that determines all properties of interest. To qualify as a dynamical system the family of maps must satisfy a composition rule to conform with the additive structure of time.
Literature
go back to reference Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover Publications, Mineola (1965) Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover Publications, Mineola (1965)
go back to reference Berger, A.: Chaos and Chance. Walter de Gruyter (2001) Berger, A.: Chaos and Chance. Walter de Gruyter (2001)
go back to reference Lorenz, E.N.: Deterministic Nonperiodic Flow. J. Atmos. Sci. 20 (1963) Lorenz, E.N.: Deterministic Nonperiodic Flow. J. Atmos. Sci. 20 (1963)
Metadata
Title
Deterministic Dynamical Systems
Author
Peter Müller
Copyright Year
2022
DOI
https://doi.org/10.1007/978-3-030-88486-4_2