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Lyapunov Dimension for Dynamical Systems in Euclidean Spaces
Н. В. Кузнецов, Volker Reitmann

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The article explains how Lyapunov exponents and Lyapunov dimension are used to study finite dimensional dynamical systems in Euclidean space. The researchers aim to simplify and clarify the connection between key works in the field. They discuss different definitions of Lyapunov exponents and Lyapunov dimension, and present an analytical method for estimating Lyapunov dimension. The method is applied to well-known dynamical systems, revealing self-excited and hidden attractors. The researchers also derive exact formulas for Lyapunov dimension.