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Chaos, Periodicity and Complexity on Dynamical Systems

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Chaos, Nonlinearity, Complexity

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 206))

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Abstract

In the setting of discrete dynamical systems (X, f) where X is a compact metric space and f is a continuous self-mapping of X into itself, we introduce two ways of appreciating how complicated the dynamics of such systems is. First through several notions of chaos like Li-Yorke and Devaney chaos, sensitive dependence of initial conditions, transitivity, Lyapunov exponents, and the second through different notions of entropy, mainly the Kolmogorov-Sinai and topological entropies. In particular Kolmogorov-Sinai is introduced in a very general way. Also we review some known relations among these notions of chaos and entropies.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Murcia, Región de Murcia, Murcia, 30100, Spain

    Francisco Balibrea

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  1. Francisco Balibrea
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  1. Department of Mechanical Engineering, Nuclear Engineering and Technology Programme Indian Institute of Technology Kanpur, Kanpur, 208016, India

    A. Sengupta Professor

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Balibrea, F. (2006). Chaos, Periodicity and Complexity on Dynamical Systems. In: Sengupta, A. (eds) Chaos, Nonlinearity, Complexity. Studies in Fuzziness and Soft Computing, vol 206. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31757-0_1

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  • DOI: https://doi.org/10.1007/3-540-31757-0_1

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