Chaos Near Resonance - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Chaos Near Resonance write by G. Haller. This book was released on 2012-12-06. Chaos Near Resonance available in PDF, EPUB and Kindle. A unified treatment of resonant problems with special emphasis on the recently discovered phenomenon of homoclinic jumping. After a survey of the necessary background, the book develops a general finite dimensional theory of homoclinic jumping, illustrating it with examples. The main mechanism of chaos near resonances is discussed in both the dissipative and the Hamiltonian context, incorporating previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse Silnikov manifolds. The results are applied to a variety of different problems, which include applications from beam oscillations, surface wave dynamics, nonlinear optics, atmospheric science and fluid mechanics.
Order and Chaos in Dynamical Astronomy
Order and Chaos in Dynamical Astronomy - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Order and Chaos in Dynamical Astronomy write by George Contopoulos. This book was released on 2013-03-14. Order and Chaos in Dynamical Astronomy available in PDF, EPUB and Kindle. This book is one of the first to provide a general overview of order and chaos in dynamical astronomy. The progress of the theory of chaos has a profound impact on galactic dynamics. It has even invaded celestial mechanics, since chaos was found in the solar system which in the past was considered as a prototype of order. The book provides a unifying approach to these topics from an author who has spent more than 50 years of research in the field. The first part treats order and chaos in general. The other two parts deal with order and chaos in galaxies and with other applications in dynamical astronomy, ranging from celestial mechanics to general relativity and cosmology.
Chaos, Resonance and Collective Dynamical Phenomena in the Solar System
Chaos, Resonance and Collective Dynamical Phenomena in the Solar System - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Chaos, Resonance and Collective Dynamical Phenomena in the Solar System write by Sylvio Ferraz-Mello. This book was released on 1992-05-31. Chaos, Resonance and Collective Dynamical Phenomena in the Solar System available in PDF, EPUB and Kindle. This symposium was devoted to a new celestial mechanics whose aim has become the study of such `objects' as the planetary system, planetary rings, the asteroidal belt, meteor swarms, satellite systems, comet families, the zodiacal cloud, the preplanetary nebula, etc. When the three-body problem is considered instead of individual orbits we are, now, looking for the topology of extended regions of its phase space. This Symposium was one step in the effort to close the ties between two scientific families: the observationally-oriented scientists and the theoretically-oriented scientists.
Resonance And Bifurcation To Chaos In Pendulum
Resonance And Bifurcation To Chaos In Pendulum - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Resonance And Bifurcation To Chaos In Pendulum write by Albert C J Luo. This book was released on 2017-12-15. Resonance And Bifurcation To Chaos In Pendulum available in PDF, EPUB and Kindle. A periodically forced mathematical pendulum is one of the typical and popular nonlinear oscillators that possess complex and rich dynamical behaviors. Although the pendulum is one of the simplest nonlinear oscillators, yet, until now, we are still not able to undertake a systematical study of periodic motions to chaos in such a simplest system due to lack of suitable mathematical methods and computational tools. To understand periodic motions and chaos in the periodically forced pendulum, the perturbation method has been adopted. One could use the Taylor series to expend the sinusoidal function to the polynomial nonlinear terms, followed by traditional perturbation methods to obtain the periodic motions of the approximated differential system.This book discusses Hamiltonian chaos and periodic motions to chaos in pendulums. This book first detects and discovers chaos in resonant layers and bifurcation trees of periodic motions to chaos in pendulum in the comprehensive fashion, which is a base to understand the behaviors of nonlinear dynamical systems, as a results of Hamiltonian chaos in the resonant layers and bifurcation trees of periodic motions to chaos. The bifurcation trees of travelable and non-travelable periodic motions to chaos will be presented through the periodically forced pendulum.
Global Transversality, Resonance and Chaotic Dynamics
Global Transversality, Resonance and Chaotic Dynamics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Global Transversality, Resonance and Chaotic Dynamics write by Albert C. J. Luo. This book was released on 2008. Global Transversality, Resonance and Chaotic Dynamics available in PDF, EPUB and Kindle. This unique book presents a different point of view on the fundamental theory of global transversality, resonance and chaotic dynamics in n -dimensional nonlinear dynamic systems. The methodology and techniques presented in this book are applicable to nonlinear dynamical systems in general. This book provides useful tools for analytical and numerical predictions of chaos in nonlinear Hamiltonian and dissipative systems. All theoretical results are strictly proved. However, the ideas presented in this book are less formal and rigorous in an informal and lively manner. The author hopes the initial ideas may give some inspirations in the field of nonlinear dynamics. With physical concepts, the author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in nonlinear dynamics. Sample Chapter(s). Chapter 1: Introduction (1,196 KB). Contents: Differential Geometry of Flows; Global Transversality in Continuous Dynamical Systems; Chaotic Layer Dynamics; Two-Dimensional Stochastic Layers; Stochasticity in Resonant Separatrix Layers; Nonlinear Dynamics on an Equi-energy Surface; Stability and Grazing in Dissipative Systems; Global Dynamics in Two-Dimensional Dynamical Systems; Flow Switchability in Discontinuous Dynamical Systems. Readership: Mathematicians, physicists, researchers and engineers in mechanical engineering and electrical engineering as well as university professors and students.
