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Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 891/5 ( reviews)

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Book Synopsis Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems by : Bernold Fiedler

Download or read book Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems written by Bernold Fiedler. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.

Computational Ergodic Theory

2005-12-08 Mathematics
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Release : 2005-12-08
Genre : Mathematics
Kind : eBook
Book Rating : 050/5 ( reviews)

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Book Synopsis Computational Ergodic Theory by : Geon Ho Choe

Download or read book Computational Ergodic Theory written by Geon Ho Choe. This book was released on 2005-12-08. Available in PDF, EPUB and Kindle. Book excerpt: Ergodic theory is hard to study because it is based on measure theory, which is a technically difficult subject to master for ordinary students, especially for physics majors. Many of the examples are introduced from a different perspective than in other books and theoretical ideas can be gradually absorbed while doing computer experiments. Theoretically less prepared students can appreciate the deep theorems by doing various simulations. The computer experiments are simple but they have close ties with theoretical implications. Even the researchers in the field can benefit by checking their conjectures, which might have been regarded as unrealistic to be programmed easily, against numerical output using some of the ideas in the book. One last remark: The last chapter explains the relation between entropy and data compression, which belongs to information theory and not to ergodic theory. It will help students to gain an understanding of the digital technology that has shaped the modern information society.

Efficient Approximation Methods for the Global Long-term Behavior of Dynamical Systems

2011
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Release : 2011
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Kind : eBook
Book Rating : 524/5 ( reviews)

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Book Synopsis Efficient Approximation Methods for the Global Long-term Behavior of Dynamical Systems by : Péter Koltai

Download or read book Efficient Approximation Methods for the Global Long-term Behavior of Dynamical Systems written by Péter Koltai. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: Fur die Analyse des Langzeitverhaltens dynamischer Systeme werden in dieser Dissertation drei neue Ansatze, basierend auf Transferoperator-Methoden, zur Entwicklung effizienter Algorithmen vorgestellt. Zuerst leiten wir eine Diskretisierung auf dunnen Gittern her, um den Fluch der Dimension in den Griff zu bekommen. Die zweite Methode behandelt den infinitesimalen Generator der Transferoperator-Halbgruppe fur zeit-kontinuierliche Systeme. Als Drittes benutzen wir mean-field-Theorie, um die Dynamik von Subsystemen zu beschreiben, wobei besonderes Augenmerk auf die Konformationsanalyse in der Molekuldynamik gerichtet wird. Des Weiteren werden Bedingungen hergeleitet, unter welchen die Galerkin-Projektion des Transferoperators mit einer kleinen zufalligen Storung des zugrunde liegenden Systems in Verbindung gebracht werden kann. In this thesis three new transfer operator based approaches are developed for the analysis of the long-term behavior of dynamical systems. First, a sparse grid discretization is derived in order to deal with the "curse of dimension". The second method considers the infinitesimal generator of the transfer operator semigroup for continuous-time systems. The third method uses mean field theory to describe the dynamics of subsystems; here the main attention is devoted to conformation analysis in molecular dynamics. Further, conditions are derived such that the Galerkin projection of the transfer operator can be related to a small random perturbation of the underlying system.

Attractor Dimension Estimates for Dynamical Systems: Theory and Computation

2020-07-02 Computers
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Release : 2020-07-02
Genre : Computers
Kind : eBook
Book Rating : 877/5 ( reviews)

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Book Synopsis Attractor Dimension Estimates for Dynamical Systems: Theory and Computation by : Nikolay Kuznetsov

Download or read book Attractor Dimension Estimates for Dynamical Systems: Theory and Computation written by Nikolay Kuznetsov. This book was released on 2020-07-02. Available in PDF, EPUB and Kindle. Book excerpt: This book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Carathéodory 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 Hénon 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.

Dynamical Systems in Theoretical Perspective

2018-09-01 Mathematics
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Release : 2018-09-01
Genre : Mathematics
Kind : eBook
Book Rating : 980/5 ( reviews)

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Book Synopsis Dynamical Systems in Theoretical Perspective by : Jan Awrejcewicz

Download or read book Dynamical Systems in Theoretical Perspective written by Jan Awrejcewicz. This book was released on 2018-09-01. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on theoretical aspects of dynamical systems in the broadest sense. It highlights novel and relevant results on mathematical and numerical problems that can be found in the fields of applied mathematics, physics, mechanics, engineering and the life sciences. The book consists of contributed research chapters addressing a diverse range of problems. The issues discussed include (among others): numerical-analytical algorithms for nonlinear optimal control problems on a large time interval; gravity waves in a reservoir with an uneven bottom; value distribution and growth of solutions for certain Painlevé equations; optimal control of hybrid systems with sliding modes; a mathematical model of the two types of atrioventricular nodal reentrant tachycardia; non-conservative instability of cantilevered nanotubes using the Cell Discretization Method; dynamic analysis of a compliant tensegrity structure for use in a gripper application; and Jeffcott rotor bifurcation behavior using various models of hydrodynamic bearings.

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