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Dimension Estimates for Dynamical Systems with Some Degree of Non-injectivity and Nonsmoothness

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Attractor Dimension Estimates for Dynamical Systems: Theory and Computation

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 38))

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Abstract

In this chapter dimension estimates for maps and dynamical systems with specific properties are derived. In Sect. 10.1 a class of non-injective smooth maps is considered. Dimension estimates for piecewise non-injective maps are given in Sect. 10.2. For piecewise smooth maps with a special singularity set upper Hausdorff dimension estimates are shown in Sect. 10.3. Lower dimension estimates are shown in Sect. 10.4.

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Authors and Affiliations

  1. Department of Applied Cybernetics, Faculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia

    Nikolay Kuznetsov & Volker Reitmann

  2. Faculty of Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Nikolay Kuznetsov

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  1. Nikolay Kuznetsov
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  2. Volker Reitmann
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Correspondence to Nikolay Kuznetsov .

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Kuznetsov, N., Reitmann, V. (2021). Dimension Estimates for Dynamical Systems with Some Degree of Non-injectivity and Nonsmoothness. In: Attractor Dimension Estimates for Dynamical Systems: Theory and Computation. Emergence, Complexity and Computation, vol 38. Springer, Cham. https://doi.org/10.1007/978-3-030-50987-3_10

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  • DOI: https://doi.org/10.1007/978-3-030-50987-3_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-50986-6

  • Online ISBN: 978-3-030-50987-3

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