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Introduction to Dimension Theory

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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))

Abstract

In Chap. 2 the dimension of a vector space was defined as the maximal number of linearly independent vectors existing in it. The simplest example of an n-dimensional space, whose dimension is understood in this sense, is the space \(\mathbb R^n\). The dimension theory, which was developed in the early 20th century, has extended this conception to more general classes of spaces and sets. In the following we give a short introduction into important notions of dimension for sets in general topological or metric spaces. We restrict ourselves to those dimensions and their properties which are especially useful in the investigation of ODE’s.

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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). Introduction to Dimension Theory. 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_3

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  • DOI: https://doi.org/10.1007/978-3-030-50987-3_3

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  • Print ISBN: 978-3-030-50986-6

  • Online ISBN: 978-3-030-50987-3

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