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Attractor Dimension Estimates for Dynamical Systems: Theory and Computation - Dedicated to Gennady Leonov (Hardcover, 1st ed.... Attractor Dimension Estimates for Dynamical Systems: Theory and Computation - Dedicated to Gennady Leonov (Hardcover, 1st ed. 2021)
Nikolay Kuznetsov, Volker Reitmann
R6,335 Discovery Miles 63 350 Ships in 12 - 19 working days

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.

Nonlinear Dynamics and Quantum Dynamical Systems - Contributions to the International Seminar ISAM-90, held in Gaussig (GDR),... Nonlinear Dynamics and Quantum Dynamical Systems - Contributions to the International Seminar ISAM-90, held in Gaussig (GDR), March 19-23,1990 (Hardcover, Reprint 2021)
Gennadij A Leonov, Volker Reitmann, Werner Timmermann
R3,469 Discovery Miles 34 690 Ships in 10 - 15 working days
Attractor Dimension Estimates for Dynamical Systems: Theory and Computation - Dedicated to Gennady Leonov (Paperback, 1st ed.... Attractor Dimension Estimates for Dynamical Systems: Theory and Computation - Dedicated to Gennady Leonov (Paperback, 1st ed. 2021)
Nikolay Kuznetsov, Volker Reitmann
R6,395 Discovery Miles 63 950 Ships in 10 - 15 working days

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.

Dimension Theory for Ordinary Differential Equations (Paperback, Softcover reprint of the original 1st ed. 2005): Vladimir A.... Dimension Theory for Ordinary Differential Equations (Paperback, Softcover reprint of the original 1st ed. 2005)
Vladimir A. Boichenko, Genadij A. Leonov, Volker Reitmann
R4,162 Discovery Miles 41 620 Ships in 10 - 15 working days

This book is devoted to the estimation of dimension-like characteristics (Hausdorff dimension, fractal dimension, Lyapunov dimension, topological entropy) for attractors (mainly global B-attractors) of ordinary differential equations, time-discrete systems and dynamical systems on finite-dimensional manifolds. The contraction under flows of parameter-dependent outer measures is shown by introducing varying Lyapunov functions or metric tensors in the calculation of singular values. For the attractors of the Henon and Lorenz systems, exact formulae for the Lyapunov dimension are derived.

Non-Local Methods for Pendulum-Like Feedback Systems (German, Paperback, Softcover reprint of the original 1st ed. 1992):... Non-Local Methods for Pendulum-Like Feedback Systems (German, Paperback, Softcover reprint of the original 1st ed. 1992)
Gennadij A Leonov; Volker Reitmann, Vera B Smirnova
R1,089 Discovery Miles 10 890 Ships in 10 - 15 working days

0 are already deecribed by I. Newton (116]. However it was 250 years later that F. Tricorni (147] carried out the first non-local qualitative investigation of equation (0.1) with arbitrary o 0 and "'{ 0. It was proved by F. Tricorni that any solution of (0.1) with o > 0 corresponds either to a rotatory motion or to a damped oscillatory motion. Moreover, he showed that in the non-trivial case "' ::: 1 there exists a bifurcation value ocr("' ) corresponding to a separatrix-loop, i.e. to a double-asymptotic to a saddle-point trajectory. For o ocr("'') global asymptotic stability takes place, i.e. every motion is a damped oscillation. The papers of F. Tricorni became familiar immediately.

Regulare Und Chaotische Dynamik (German, Paperback, 1996 ed.): Volker Reitmann Regulare Und Chaotische Dynamik (German, Paperback, 1996 ed.)
Volker Reitmann
R1,268 Discovery Miles 12 680 Ships in 10 - 15 working days

Das Buch enthalt eine kompakte Darstellung wichtiger Elemente der nichtlinearen Dynamik, die von Attraktoren, invarianten Mannigfaltigkeiten und der Stabilitat des Orbits in zeitkontinuierlichen und zeitdiskreten Bifurkationen bis hin zu Shifts, Hufeisen, invarianten Massen, Entropien und Dimensionen in dynamischen Systemen reicht. Die wichtigsten Routen dynamischer Systeme ins Chaos werden vorgestellt."

Attraktoreingrenzung fur nichtlineare Systeme (German, Paperback, 1987 ed.): Gennadij A Leonov Attraktoreingrenzung fur nichtlineare Systeme (German, Paperback, 1987 ed.)
Gennadij A Leonov; Volker Reitmann
R1,853 Discovery Miles 18 530 Ships in 10 - 15 working days

Dieses Buch ist der Attraktorapproximation solcher endlich- dimensionaler dynamischer Systeme gewidmet, die in Verbindung mit der Turbulenztheorie in den letzten Jahren besonderes Inter- esse hervorrufen. Es stellt einen Versuch dar, fur bekannte Dif- ferentialgleichungssysteme wie das Lorenz-System, das Roesslar- System und damit verbundene diskrete Systeme durch Anwendung der direkten Methode von Ljapunow, der Tschaplygin-Methode, der nichtlinearen Reduktionsmethode und anderer Methoden bestimmte Aussagen UEber das LOEsungsverhalten dieser Systeme zu erhalten. In der Regel gelingt es dabei, Stabilitatseigenschaften zu for- mulieren und Obermengen fur die vorwiegend komplizierten Attrak- toren der betrachteten Systeme zu konstruieren. Diese Obermengen kOEnnen auch zum Nachweis der Existenz von Separatrixschlingen und von Abschatzungen der Parameter, die Separatrixschlingen entsprechen, genutzt werden. Mit dem vorliegenden Buch soll keine EinfUEhrung in die Gesamt- problematik der Chaos-Theorie gegeben werden, da es hierzu be- reits eine ganze Reihe von Publikationen gibt, in denen ver- schiedene Aspekte dieser Entwicklungsrichtung dargestellt sind 1 1 [8, 50, 58, 76, 81, 109, 117, 118, 118, 120, 130]. Im Unter- schied zur vorhandenen Literatur werden-in diesem Buch verstarkt die oben erwahnten Methoden eingesetzt. Es ist die Oberzeugung 11 der Autoren, dass durch Approximation der Attraktoren von aussen 11 11 und Organisation der Instabilitat uvon innen auf der Basis der im Buch diskutierten Methoden ein effektiver Zugang zum analyti- schen Nachweis seltsamer Attraktoren fur dynamische Systeme ge- funden werden kann. Mit den im Buch enthaltenen Ergebnissen soll ein Schritt in dieser Richtung getan werden.

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