Topology And Dynamics Of Chaos: In Celebration Of Robert Gilmore's 70th Birthday

Topology And Dynamics Of Chaos: In Celebration Of Robert Gilmore's 70th Birthday
Title Topology And Dynamics Of Chaos: In Celebration Of Robert Gilmore's 70th Birthday PDF eBook
Author Christophe Letellier
Publisher World Scientific
Pages 362
Release 2013-01-11
Genre Mathematics
ISBN 9814434876

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The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included.The contents are mainly devoted to topology, the main field of Robert Gilmore's works in dynamical systems. They include a review on the topological analysis of chaotic dynamics, works done in the past as well as the very latest issues. Most of the contributors who published during the 90's, including the very well-known scientists Otto Rössler, René Lozi and Joan Birman, have made a significant impact on chaos theory, discrete chaos, and knot theory, respectively.Very few books cover the topological approach for investigating nonlinear dynamical systems. The present book will provide not only some historical — not necessarily widely known — contributions (about the different types of chaos introduced by Rössler and not just the “Rössler attractor”; Gumowski and Mira's contributions in electronics; Poincaré's heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology, etc.

Topological Methods for Delay and Ordinary Differential Equations

Topological Methods for Delay and Ordinary Differential Equations
Title Topological Methods for Delay and Ordinary Differential Equations PDF eBook
Author Pablo Amster
Publisher Springer Nature
Pages 220
Release
Genre
ISBN 3031613376

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Encyclopedia of Knot Theory

Encyclopedia of Knot Theory
Title Encyclopedia of Knot Theory PDF eBook
Author Colin Adams
Publisher CRC Press
Pages 1048
Release 2021-02-10
Genre Mathematics
ISBN 100022242X

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"Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject." – Ed Witten, Recipient of the Fields Medal "I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It’s a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field." – Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis Knot theory has proven to be a fascinating area of mathematical research, dating back about 150 years. Encyclopedia of Knot Theory provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications. Many of the articles in this book are accessible to undergraduates who are working on research or taking an advanced undergraduate course in knot theory. More advanced articles will be useful to graduate students working on a related thesis topic, to researchers in another area of topology who are interested in current results in knot theory, and to scientists who study the topology and geometry of biopolymers. Features Provides material that is useful and accessible to undergraduates, postgraduates, and full-time researchers Topics discussed provide an excellent catalyst for students to explore meaningful research and gain confidence and commitment to pursuing advanced degrees Edited and contributed by top researchers in the field of knot theory

Chaos In Nature (Second Edition)

Chaos In Nature (Second Edition)
Title Chaos In Nature (Second Edition) PDF eBook
Author Christophe Letellier
Publisher World Scientific
Pages 437
Release 2019-04-26
Genre Science
ISBN 9811201218

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This book is devoted to the history of chaos theory, from celestial mechanics (three-body problem) to electronics and meteorology. Many illustrative examples of chaotic behaviors exist in various contexts found in nature (chemistry, astrophysics, biomedicine). This book includes the most popular systems from chaos theory (Lorenz, Rössler, van der Pol, Duffing, logistic map, Lozi map, Hénon map etc.) and introduces many other systems, some of them very rarely discussed in textbooks as well as in scientific papers. The contents are formulated with an original approach as compared to other books on chaos theory.

Coupled Phase-locked Loops: Stability, Synchronization, Chaos And Communication With Chaos

Coupled Phase-locked Loops: Stability, Synchronization, Chaos And Communication With Chaos
Title Coupled Phase-locked Loops: Stability, Synchronization, Chaos And Communication With Chaos PDF eBook
Author Valery V Matrosov
Publisher World Scientific
Pages 255
Release 2018-08-29
Genre Science
ISBN 9813271965

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Modern technological, biological, and socioeconomic systems are extremely complex. The study of such systems largely relies on the concepts of competition and cooperation (synchronization). The main approaches to the study of nonlinear dynamics of complex systems are now associated with models of collective dynamics of networks and ensembles, formed by interacting dynamical elements.Unfortunately, the applicability of analytical and qualitative methods of nonlinear dynamics to such complex systems is severely restricted due to the high dimension of phase space. Therefore, studying the simplest models of networks, which are ensembles with a small number of elements, becomes of particular interest. Such models allow to make use of the entire spectrum of analytical, qualitative, and numerical methods of nonlinear dynamics. This book is devoted to the investigation of a kind of such systems, namely small ensembles of coupled, phase-controlled oscillators. Both traditional issues, like synchronization, that are relevant for applications in radio-communications, radio-location, energy, etc., and nontraditional issues of excitation of chaotic oscillations and their possible application in advanced communication systems are addressed.

Deterministic Chaos In One Dimensional Continuous Systems

Deterministic Chaos In One Dimensional Continuous Systems
Title Deterministic Chaos In One Dimensional Continuous Systems PDF eBook
Author Jan Awrejcewicz
Publisher World Scientific
Pages 577
Release 2016-03-14
Genre Science
ISBN 9814719714

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This book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time. The reduction is carried out based on a formal mathematical approach aimed at reducing the problems with infinite dimension to finite ones. The process also includes a transition from governing nonlinear partial differential equations to a set of finite number of ordinary differential equations.Beginning with an overview of the recent results devoted to the analysis and control of nonlinear dynamics of structural members, placing emphasis on stability, buckling, bifurcation and deterministic chaos, simple chaotic systems are briefly discussed. Next, bifurcation and chaotic dynamics of the Euler-Bernoulli and Timoshenko beams including the geometric and physical nonlinearity as well as the elastic-plastic deformations are illustrated. Despite the employed classical numerical analysis of nonlinear phenomena, the various wavelet transforms and the four Lyapunov exponents are used to detect, monitor and possibly control chaos, hyper-chaos, hyper-hyper-chaos and deep chaos exhibited by rectangular plate-strips and cylindrical panels.The book is intended for post-graduate and doctoral students, applied mathematicians, physicists, teachers and lecturers of universities and companies dealing with a nonlinear dynamical system, as well as theoretically inclined engineers of mechanical and civil engineering.

Toward General Theory Of Differential-operator And Kinetic Models

Toward General Theory Of Differential-operator And Kinetic Models
Title Toward General Theory Of Differential-operator And Kinetic Models PDF eBook
Author Nikolay Sidorov
Publisher World Scientific
Pages 495
Release 2020-03-13
Genre Science
ISBN 9811213763

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This volume provides a comprehensive introduction to the modern theory of differential-operator and kinetic models including Vlasov-Maxwell, Fredholm, Lyapunov-Schmidt branching equations to name a few. This book will bridge the gap in the considerable body of existing academic literature on the analytical methods used in studies of complex behavior of differential-operator equations and kinetic models. This monograph will be of interest to mathematicians, physicists and engineers interested in the theory of such non-standard systems.