Paperback. 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. 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. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

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Titolo: Attractor Dimension Estimates for Dynamical Systems: Theory and Computation (Paperback)
Editore: Springer Nature Switzerland AG, Cham
Data di pubblicazione: 2021
Lingua: Inglese
ISBN 10: 3030509893
ISBN 13: 9783030509897
Rilegatura: Paperback
Condizione: new

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This book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Carath�odory 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 H�non 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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