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Deterministic Dynamical Systems

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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.

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  • DOI: 10.1007/978-3-030-88486-4_2
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References

  • Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover Publications, Mineola (1965)

    Google Scholar 

  • Berger, A.: Chaos and Chance. Walter de Gruyter (2001)

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  • Lorenz, E.N.: Deterministic Nonperiodic Flow. J. Atmos. Sci. 20 (1963)

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Correspondence to Peter Müller .

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Müller, P. (2022). Deterministic Dynamical Systems. In: Handbook of Dynamics and Probability. Springer, Cham. https://doi.org/10.1007/978-3-030-88486-4_2

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