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Author: Jacob Palis Júnior
Publisher: Cambridge University Press
Published: 1995-01-05
Total Pages: 248
ISBN-13: 9780521475723
DOWNLOAD EBOOK →A self-contained introduction to the classical theory and its generalizations, aimed at mathematicians and scientists working in dynamical systems.
Author: Ale Jan Homburg
Publisher: American Mathematical Soc.
Published: 1996
Total Pages: 128
ISBN-13: 0821804413
DOWNLOAD EBOOK →In this book, the author investigates a class of smooth one parameter families of vector fields on some $n$-dimensional manifold, exhibiting a homoclinic bifurcation. That is, he considers generic families $x_\mu$, where $x_0$ has a distinguished hyperbolic singularity $p$ and a homoclinic orbit; an orbit converging to $p$ both for positive and negative time. It is assumed that this homoclinic orbit is of saddle-saddle type, characterized by the existence of well-defined directions along which it converges to the singularity $p$. The study is not confined to a small neighborhood of the homoclinic orbit. Instead, the position of the stable and unstable set of the homoclinic orbit is incorporated and it is shown that homoclinic bifurcations can lead to complicated bifurcations and dynamics, including phenomena like intermittency and annihilation of suspended horseshoes.
Author: I︠U︡. S. Ilʹi︠a︡shenko
Publisher: American Mathematical Soc.
Published: 1999
Total Pages: 303
ISBN-13: 0821804979
DOWNLOAD EBOOK →This book studies nonlocal bifurcations that occur on the boundary of the domain of Morse-Smale systems in the space of all dynamical systems. These bifurcations provide a series of fascinating new scenarios for the transition from simple dynamical systems to complicated ones. The main effects are the generation of hyperbolic periodic orbits, nontrivial hyperbolic invariant sets and the elements of hyperbolic theory. All results are rigorously proved and exposed in a uniform way. The foundations of normal forms and hyperbolic theories are presented from the very first stages. The proofs are preceded by heuristic descriptions of the ideas. The book contains new results, and many results have not previously appeared in monograph form.
Author: Christian Bonatti
Publisher: Springer Science & Business Media
Published: 2006-03-30
Total Pages: 390
ISBN-13: 3540268448
DOWNLOAD EBOOK →What is Dynamics about? In broad terms, the goal of Dynamics is to describe the long term evolution of systems for which an "infinitesimal" evolution rule is known. Examples and applications arise from all branches of science and technology, like physics, chemistry, economics, ecology, communications, biology, computer science, or meteorology, to mention just a few. These systems have in common the fact that each possible state may be described by a finite (or infinite) number of observable quantities, like position, velocity, temperature, concentration, population density, and the like. Thus, m the space of states (phase space) is a subset M of an Euclidean space M . Usually, there are some constraints between these quantities: for instance, for ideal gases pressure times volume must be proportional to temperature. Then the space M is often a manifold, an n-dimensional surface for some n
Author: A. Katok
Publisher: Elsevier
Published: 2005-12-17
Total Pages: 1235
ISBN-13: 0080478220
DOWNLOAD EBOOK →This second half of Volume 1 of this Handbook follows Volume 1A, which was published in 2002. The contents of these two tightly integrated parts taken together come close to a realization of the program formulated in the introductory survey “Principal Structures of Volume 1A.The present volume contains surveys on subjects in four areas of dynamical systems: Hyperbolic dynamics, parabolic dynamics, ergodic theory and infinite-dimensional dynamical systems (partial differential equations). . Written by experts in the field.. The coverage of ergodic theory in these two parts of Volume 1 is considerably more broad and thorough than that provided in other existing sources. . The final cluster of chapters discusses partial differential equations from the point of view of dynamical systems.
Author: H.W Broer
Publisher: CRC Press
Published: 2001-06-18
Total Pages: 498
ISBN-13: 9781420034288
DOWNLOAD EBOOK →Contributed by close colleagues, friends, and former students of Floris Takens, Global Analysis of Dynamical Systems is a liber amicorum dedicated to Takens for his 60th birthday. The first chapter is a reproduction of Takens's 1974 paper "Forced oscillators and bifurcations" that was previously available only as a preprint of the University of Utrecht. Among other important results, it contains the unfolding of what is now known as the Bogdanov-Takens bifurcation. The remaining chapters cover topics as diverse as bifurcation theory, Hamiltonian mechanics, homoclinic bifurcations, routes to chaos, ergodic theory, renormalization theory, and time series analysis. In its entirety, the book bears witness to the influence of Takens on the modern theory of dynamical systems and its applications. This book is a must-read for anyone interested in this active and exciting field.
Author: Inman Harvey
Publisher: Springer Science & Business Media
Published: 2013-03-23
Total Pages: 215
ISBN-13: 1461464099
DOWNLOAD EBOOK →SmartData empowers personal data by wrapping it in a cloak of intelligence such that it now becomes the individual’s virtual proxy in cyberspace. No longer will personal data be shared or stored in the cloud as merely data, encrypted or otherwise; it will now be stored and shared as a constituent of the binary string specifying the entire SmartData agent. This agent proactively builds-in privacy, security and user preferences, right from the outset, not as an afterthought. SmartData: Privacy Meets Evolutionary Robotics includes the advances made in the technology of simulating virtual worlds, together with the ideas emerging from fields of evolutionary robotics and embodied cognition within a framework of dynamical systems as an approach toward this ultimate goal. The book brings together top researchers in the field and addresses current personal data privacy challenges in the online-world.
Author: Stephen Wiggins
Publisher: Springer Science & Business Media
Published: 2013-11-27
Total Pages: 505
ISBN-13: 1461210429
DOWNLOAD EBOOK →Global Bifurcations and Chaos: Analytical Methods is unique in the literature of chaos in that it not only defines the concept of chaos in deterministic systems, but it describes the mechanisms which give rise to chaos (i.e., homoclinic and heteroclinic motions) and derives explicit techniques whereby these mechanisms can be detected in specific systems. These techniques can be viewed as generalizations of Melnikov's method to multi-degree of freedom systems subject to slowly varying parameters and quasiperiodic excitations. A unique feature of the book is that each theorem is illustrated with drawings that enable the reader to build visual pictures of global dynamcis of the systems being described. This approach leads to an enhanced intuitive understanding of the theory.
