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Attractor Dimension Estimates for Dynamical Systems: Theory and Computation - Dedicated to Gennady Leonov (Hardcover, 1st ed. 2021)
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Attractor Dimension Estimates for Dynamical Systems: Theory and Computation - Dedicated to Gennady Leonov (Hardcover, 1st ed. 2021)
Series: Emergence, Complexity and Computation, 38
Expected to ship within 12 - 19 working days
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This book provides analytical and numerical methods for the
estimation of dimension characteristics (Hausdorff, Fractal,
Caratheodory dimensions) for attractors and invariant sets of
dynamical systems and cocycles generated by smooth differential
equations or maps in finite-dimensional Euclidean spaces or on
manifolds. It also discusses stability investigations using
estimates based on Lyapunov functions and adapted metrics.
Moreover, it introduces various types of Lyapunov dimensions of
dynamical systems with respect to an invariant set, based on local,
global and uniform Lyapunov exponents, and derives analytical
formulas for the Lyapunov dimension of the attractors of the Henon
and Lorenz systems. Lastly, the book presents estimates of the
topological entropy for general dynamical systems in metric spaces
and estimates of the topological dimension for orbit closures of
almost periodic solutions to differential equations.
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