Описание: The study of dynamical systems is a well established field. Having given graduate-level courses on the subject for many years, the authors have now written this book to provide a panorama of the aspects that are of interest to mathematicians and physicists alike. Avoiding belaboured proofs, the exposition concentrates instead on abundant illustrations and examples, while still retaining sufficient mathematical precision. Besides the standard topics of the field, questions of physical measurement and stochastic properties of chaotic dynamical systems are given much attention.
Описание: Chaos theory plays an important role in modern physics and related sciences, but -, the most important results so far have been obtained in the study of gravitational systems applied to celestial mechanics. The present set of lectures introduces the mathematical methods used in the theory of singularities in gravitational systems, reviews modeling techniques for the simulation of close encounters and presents the state of the art about the study of diffusion of comets, wandering asteroids, meteors and planetary ring particles. The book will be of use to researchers and graduate students alike.
Автор: Landa Polina S. Название: Regular and Chaotic Oscillations ISBN: 3540410015 ISBN-13(EAN): 9783540410010 Издательство: Springer Рейтинг: Цена: 19056 р. Наличие на складе: Поставка под заказ.
Описание: In this book the modern theory of both regular and chaotic nonlinear oscillations is set out, primarily, as applied to mechanical problems. The material is presented in a nontraditional manner with emphasis on the new results of the theory obtained partially by the author, who is one of the leading experts in the area. Among the up-to-date topics are synchronization and chaotization of self-oscillatory systems and the influence of weak random vibrations on the modification of characteristics and behavior of nonlinear systems. One of the purposes of the book is to enable readers to gain a thorough understanding of this theory and to show that it can be very useful in engineering investigations. The primary audience for this book is researchers working with different oscillatory processes and students interested in a thorough study of the general laws and applications of the theory of nonlinear oscillations.
Автор: Tam?s T?l Название: Chaotic Dynamics ISBN: 0521547830 ISBN-13(EAN): 9780521547833 Издательство: Cambridge Academ Рейтинг: Цена: 8490 р. Наличие на складе: Поставка под заказ.
Описание: In the past few decades we have come to understand that even motions in simple systems can have complex and surprising properties. Chaotic Dynamics provides a clear introduction to these chaotic phenomena, based on geometrical interpretations and simple arguments, without the need for prior in-depth scientific and mathematical knowledge. Richly illustrated throughout, examples are taken from classical mechanics whose elementary laws are familiar to the reader. In order to emphasize the general features of chaos, the most important relations are also given in simple mathematical forms, independent of any mechanical interpretation. A broad range of potential applications are presented, ranging from everyday phenomena through engineering and environmental problems to astronomical aspects. Chaos occurs in a variety of scientific disciplines, and proves to be the rule, not the exception. This book is primarily intended for undergraduate students in science, engineering, and mathematics.
Описание: The interest of the applied mechanics community towards chaotic dynamics of engineering systems has exploded in the last fifteen years. Today, it is generally accepted that nonlinear vibration problems of advanced systems should be addressed through the combined use of analytical, computational, geometrical and experimental approaches, by paying also attention to the interaction with control features. The outstanding points of these proceedings are a coherent compendium of the current state of theory and applications of nonlinear and chaotic dynamics in mechanics, along with their control. Subject areas include: Bifurcation and chaos, mechanical and structural systems, nonsmooth dynamics, delay and random systems, control of systems and processes, synchronization and control of chaos.Major achievements are highlighted as regards: Complex systems and processes for classical and innovative applications, features of nonlinear interactions, patterns of novel bifurcations of non-smooth systems, dimensionality and reduced-order models of continuous systems, exploitation of dynamical systems properties for applications, implications of chaos for design and operating conditions, control of spatio-temporal dynamics.For scientists from Engineering and Physics communities, this book will provide first-hand information on recent developments in nonlinear dynamics, chaos and control of mechanical systems and processes.
Автор: Vialar, Thierry Название: Complex and chaotic nonlinear dynamics ISBN: 3540859772 ISBN-13(EAN): 9783540859772 Издательство: Springer Рейтинг: Цена: 24140 р. Наличие на складе: Поставка под заказ.
Описание: Complex dynamics constitute a growing and increasingly important area as they offer a strong potential to explain and formalize natural, physical, financial and economic phenomena. This book pursues the goal to bring together a body of knowledge regarding complex dynamics from various academic disciplines.
Описание: The physics and mathematics of nonlinear dynamics and chaotic and complex systems constitute some of the most fascinating developments of late twentieth-century science. It turns out that chaotic behaviour can be understood, and even utilized, to a far greater degree than had been suspected. Surprisingly, universal constants have been discovered. The implications have changed our understanding of important phenomena in physics, biology, chemistry, economics, medicine and numerous other fields of human endeavour. In this book, two dozen scientists and mathematicians who were deeply involved in the ‘nonlinear revolution’ cover most of the basic aspects of the field. The book is divided into five parts: dynamical systems, bifurcation theory and chaos; spatially extended systems; dynamical chaos, quantum physics and the foundations of statistical mechanics; evolutionary and cognitive systems; and complex systems as an interface between the sciences.
Автор: Goodson Название: Chaotic Dynamics ISBN: 1107112672 ISBN-13(EAN): 9781107112674 Издательство: Cambridge Academ Рейтинг: Цена: 6983 р. Наличие на складе: Поставка под заказ.
Описание: This undergraduate textbook is a rigorous mathematical introduction to dynamical systems and an accessible guide for students transitioning from calculus to advanced mathematics. It has many student-friendly features, such as graded exercises that range from straightforward to more difficult with hints, and includes concrete applications of real analysis and metric space theory to dynamical problems. Proofs are complete and carefully explained, and there is opportunity to practice manipulating algebraic expressions in an applied context of dynamical problems. After presenting a foundation in one-dimensional dynamical systems, the text introduces students to advanced subjects in the latter chapters, such as topological and symbolic dynamics. It includes two-dimensional dynamics, Sharkovsky's theorem, and the theory of substitutions, and takes special care in covering Newton's method. Mathematica code is available online, so that students can see implementation of many of the dynamical aspects of the text.
Описание: The work done in chaotic modeling and simulation has changed our views of the world around us and has introduced scientific tools, methods and techniques. This book includes advanced topics of these achievements on Chaos Theory which focuses on Chaotic Modeling, Simulation and Applications of the nonlinear phenomena.
Автор: Gitterman Moshe Название: Chaotic Pendulum ISBN: 9814322008 ISBN-13(EAN): 9789814322003 Издательство: World Scientific Publishing Рейтинг: Цена: 9723 р. Наличие на складе: Поставка под заказ.
Описание: Pendulum is the simplest nonlinear system, which, however, provides the means for the description of different phenomena in Nature that occur in physics, chemistry, biology, medicine, communications, economics and sociology. This book presents a comprehensive description of these phenomena going on in underdamped and overdamped pendula.
Описание: The gravitational N-body problem dominates much of theoretical astrophysics. It arises in problems ranging from the motion of artificial and natural satellites to the behaviour of stars in star clusters and galaxies. In the past, research in Celestial Mechanics has focused on analytical and numerical studies of ordered systems, with chaotic behaviour or disorder being the fascinating anomaly. Recently, however, scientists have begun to forge the link between order and disorder: designing new methods to recognise chaosвЂ™ signature and developing new theories on the sources of chaotic behaviour. They are applying these techniques successfully to solve real-world problems in solar system dynamics, galactic dynamics and other areas of physics such as particle acceleration. Based on the recent NATO Advanced Study Institute "Chaotic Worlds: From Order to Disorder in Gravitational N-Body Dynamical Systems", this state of the art textbook, written by internationally renowned experts, provides an invaluable reference volume for all students and researchers in gravitational n-body systems. The contributions are especially designed to give a systematic development from the fundamental mathematics which underpin modern studies of ordered and chaotic behaviour in n-body dynamics to their application to real motion in planetary systems. This volume presents an up-to-date synoptic view of the subject.
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