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Chaotic and Fractal Dynamics

2008-11-20 Science
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Release : 2008-11-20
Genre : Science
Kind : eBook
Book Rating : 515/5 ( reviews)

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Book Synopsis Chaotic and Fractal Dynamics by : Francis C. Moon

Download or read book Chaotic and Fractal Dynamics written by Francis C. Moon. This book was released on 2008-11-20. Available in PDF, EPUB and Kindle. Book excerpt: A revision of a professional text on the phenomena of chaotic vibrations in fluids and solids. Major changes reflect the latest developments in this fast-moving topic, the introduction of problems to every chapter, additional mathematics and applications, more coverage of fractals, numerous computer and physical experiments. Contains eight pages of 4-color pictures.

Chaotic and Fractal Dynamics

1992 Mathematics
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Release : 1992
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Chaotic and Fractal Dynamics by : F. C. Moon

Download or read book Chaotic and Fractal Dynamics written by F. C. Moon. This book was released on 1992. Available in PDF, EPUB and Kindle. Book excerpt: A revision of a professional text on the phenomena of chaotic vibrations in fluids and solids. Major changes reflect the latest developments in this fast-moving topic, the introduction of problems to every chapter, additional mathematics and applications, more coverage of fractals, numerous computer and physical experiments. Contains eight pages of 4-color pictures.

Chaotic Dynamics and Fractals

2014-05-10 Mathematics
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Release : 2014-05-10
Genre : Mathematics
Kind : eBook
Book Rating : 086/5 ( reviews)

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Book Synopsis Chaotic Dynamics and Fractals by : Michael F. Barnsley

Download or read book Chaotic Dynamics and Fractals written by Michael F. Barnsley. This book was released on 2014-05-10. Available in PDF, EPUB and Kindle. Book excerpt: Chaotic Dynamics and Fractals covers the proceedings of the 1985 Conference on Chaotic Dynamics, held at the Georgia Institute of Technology. This conference deals with the research area of chaos, dynamical systems, and fractal geometry. This text is organized into three parts encompassing 16 chapters. The first part describes the nature of chaos and fractals, the geometric tool for some strange attractors, and other complicated sets of data associated with chaotic systems. This part also considers the Henon-Hiles Hamiltonian with complex time, a Henon family of maps from C2 into itself, and the idea of turbulent maps in the course of presenting results on iteration of continuous maps from the unit interval to itself. The second part discusses complex analytic dynamics and associated fractal geometry, specifically the bursts into chaos, algorithms for obtaining geometrical and combinatorial information, and the parameter space for iterated cubic polynomials. This part also examines the differentiation of Julia sets with respects to a parameter in the associated rational map, permitting the formulation of Taylor series expansion for the sets. The third part highlights the applications of chaotic dynamics and fractals. This book will prove useful to mathematicians, physicists, and other scientists working in, or introducing themselves to, the field.

Dynamics with Chaos and Fractals

2020-01-01 Mathematics
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Release : 2020-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 542/5 ( reviews)

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Book Synopsis Dynamics with Chaos and Fractals by : Marat Akhmet

Download or read book Dynamics with Chaos and Fractals written by Marat Akhmet. This book was released on 2020-01-01. Available in PDF, EPUB and Kindle. Book excerpt: The book is concerned with the concepts of chaos and fractals, which are within the scopes of dynamical systems, geometry, measure theory, topology, and numerical analysis during the last several decades. It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. This is the first time in the literature that the description of chaos is initiated from a single motion. Chaos is now placed on the line of oscillations, and therefore, it is a subject of study in the framework of the theories of dynamical systems and differential equations, as in this book. The techniques introduced in the book make it possible to develop continuous and discrete dynamics which admit fractals as points of trajectories as well as orbits themselves. To provide strong arguments for the genericity of chaos in the real and abstract universe, the concept of abstract similarity is suggested.

Chaos, Fractals, and Noise

2013-11-27 Mathematics
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Release : 2013-11-27
Genre : Mathematics
Kind : eBook
Book Rating : 86X/5 ( reviews)

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Book Synopsis Chaos, Fractals, and Noise by : Andrzej Lasota

Download or read book Chaos, Fractals, and Noise written by Andrzej Lasota. This book was released on 2013-11-27. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this book was originally published in 1985 under the ti tle "Probabilistic Properties of Deterministic Systems. " In the intervening years, interest in so-called "chaotic" systems has continued unabated but with a more thoughtful and sober eye toward applications, as befits a ma turing field. This interest in the serious usage of the concepts and techniques of nonlinear dynamics by applied scientists has probably been spurred more by the availability of inexpensive computers than by any other factor. Thus, computer experiments have been prominent, suggesting the wealth of phe nomena that may be resident in nonlinear systems. In particular, they allow one to observe the interdependence between the deterministic and probabilistic properties of these systems such as the existence of invariant measures and densities, statistical stability and periodicity, the influence of stochastic perturbations, the formation of attractors, and many others. The aim of the book, and especially of this second edition, is to present recent theoretical methods which allow one to study these effects. We have taken the opportunity in this second edition to not only correct the errors of the first edition, but also to add substantially new material in five sections and a new chapter.

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