Hamiltonian Chaos And Fractional Dynamics
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Hamiltonian Chaos and Fractional Dynamics
The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology. The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics. The book does not follow the traditional scheme of most of today's literature on chaos. The intention of the author has been to put together some of the most complex and yet open problems on the general theory of chaotic systems. The importance of the discussed issues and an understanding of their origin should inspire students and researchers to touch upon some of the deepest aspects of nonlinear dynamics. The book considers the basic principles of the Hamiltonian theory of chaos and some applications including for example, the cooling of particles and signals, control and erasing of chaos, polynomial complexity, Maxwell's Demon, and others. It presents a new and realistic image of the origin of dynamical chaos and randomness. An understanding of the origin of randomness in dynamical systems, which cannot be of the same origin as chaos, provides new insights in the diverse fields of physics, biology, chemistry, and engineering.
Long-range Interactions, Stochasticity and Fractional Dynamics
Author: Albert C. J. Luo
language: en
Publisher: Springer Science & Business Media
Release Date: 2011-01-04
In memory of Dr. George Zaslavsky, "Long-range Interactions, Stochasticity and Fractional Dynamics" covers the recent developments of long-range interaction, fractional dynamics, brain dynamics and stochastic theory of turbulence, each chapter was written by established scientists in the field. The book is dedicated to Dr. George Zaslavsky, who was one of three founders of the theory of Hamiltonian chaos. The book discusses self-similarity and stochasticity and fractionality for discrete and continuous dynamical systems, as well as long-range interactions and diluted networks. A comprehensive theory for brain dynamics is also presented. In addition, the complexity and stochasticity for soliton chains and turbulence are addressed. The book is intended for researchers in the field of nonlinear dynamics in mathematics, physics and engineering. Dr. Albert C.J. Luo is a Professor at Southern Illinois University Edwardsville, USA. Dr. Valentin Afraimovich is a Professor at San Luis Potosi University, Mexico.
Fractional Dynamics
Author: Carlo Cattani
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2015-01-01
The book is devoted to recent developments in the theory of fractional calculus and its applications. Particular attention is paid to the applicability of this currently popular research field in various branches of pure and applied mathematics. In particular, the book focuses on the more recent results in mathematical physics, engineering applications, theoretical and applied physics as quantum mechanics, signal analysis, and in those relevant research fields where nonlinear dynamics occurs and several tools of nonlinear analysis are required. Dynamical processes and dynamical systems of fractional order attract researchers from many areas of sciences and technologies, ranging from mathematics and physics to computer science.