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Dynamical Systems
This volume contains original research papers on topics central to Dynamical Systems, such as fractional dimensions (Hausdorff dimension, limity capacity) and limit cycles of polynomial vector fields concerning the well-known Dulac and Hilbert's 16th problems. Stability and bifurcations, intermittency, normal forms, Anosov flows and foliations are also themes treated in the papers. Many of the authors are renowned for their important contributions to the field. This volume should be of much interest to people working in dynamical systems, including, physicists, biologists and engineers.
Chaos and Order in Nature
This book contains the invited papers of an international symposium on synergetics; which was held at Schlol3 Elmau, Bavaria, FRG, April 27 to May 1, 1981. At our previous meetings on synergetics the self-organized formation of structures in quite different disciplines stood in the foreground of our interest. More recently it has turned out that phenomena characterized by the word "chaos" appear in various disciplines, and again far-reaching analogies in the behavior of quite different systems become visible. Therefore this meeting was devoted not only to problems connected with the occurrence of ordered structures but also to most recent results obtained in the study of chaotic motion. In t...
Stochasticity and Quantum Chaos
These are the proceedings of the Third Max Born Symposium which took place at SobOtka Castle in September 1993. The Symposium is organized annually by the Institute of Theoretical Physics of the University of Wroclaw. Max Born was a student and later on an assistant at the University of Wroclaw (Wroclaw belonged to Germany at this time and was called Breslau). The topic of the Max Born Sympo sium varies each year reflecting the developement of theoretical physics. The subject of this Symposium "Stochasticity and quantum chaos" may well be considered as a continuation of the research interest of Max Born. Recall that Born treats his "Lectures on the mechanics of the atom" (published in 1925) ...
Dynamics and Randomness
This book contains the lectures given at the Conference on Dynamics and Randomness held at the Centro de Modelamiento Matematico of the Universidad de Chile from December 11th to 15th, 2000. This meeting brought together mathematicians, theoretical physicists and theoretical computer scientists, and graduate students interested in fields re lated to probability theory, ergodic theory, symbolic and topological dynam ics. We would like to express our gratitude to all the participants of the con ference and to the people who contributed to its organization. In particular, to Pierre Collet, Bernard Host and Mike Keane for their scientific advise. VVe want to thank especially the authors of each ...
Many-Particle Dynamics and Kinetic Equations
As our title suggests, there are two aspects in the subject of this book. The first is the mathematical investigation of the dynamics of infinite systems of in teracting particles and the description of the time evolution of their states. The second is the rigorous derivation of kinetic equations starting from the results of the aforementioned investigation. As is well known, statistical mechanics started in the last century with some papers written by Maxwell and Boltzmann. Although some of their statements seemed statistically obvious, we must prove that they do not contradict what me chanics predicts. In some cases, in particular for equilibrium states, it turns out that mechanics easily ...
New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena
The basic aim of the NATO Advanced Research Workshop on "New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena: The Geometry of Nonequilibrium" was to bring together researchers from various areas of physics to review and explore new ideas regarding the organisation of systems driven far from equilibrium. Such systems are characterized by a close relationship between broken spatial and tempo ral symmetries. The main topics of interest included pattern formation in chemical systems, materials and convection, traveling waves in binary fluids and liquid crystals, defects and their role in the disorganisa tion of structures, spatio-temporal intermittency, instabilities and large-scale v...
Nonlinear Dynamics and Spatial Complexity in Optical Systems
A collection of prestigious postgraduate lectures, Nonlinear Dynamics and Spatial Complexity in Optical Systems reviews developments in the theory and practice of nonlinear dynamics and structural complexity, and explores modern-day applications in nonlinear optics. The book addresses systems including both singlemode and multimode lasers, bistable and multistable devices, optical fibers, counter-propagating beam interactions, nonlinear mixing, and related optical phenomena.
Nonlinear Dynamics: Materials, Theory and Experiments
This book presents recent advances, new ideas and novel techniques related to the field of nonlinear dynamics, including localized pattern formation, self-organization and chaos. Various natural systems ranging from nonlinear optics to mechanics, fluids and magnetic are considered. The aim of this book is to gather specialists from these various fields of research to promote cross-fertilization and transfer of knowledge between these active research areas. In particular, nonlinear optics and laser physics constitute an important part in this issue due to the potential applications for all-optical control of light, optical storage, and information processing. Other possible applications include the generation of ultra-short pulses using all-fiber cavities.
Instabilities and Nonequilibrium Structures IX
This volume contains a selection of lectures and seminars given at the Ninth International Workshop on Instabilities and Nonequilibrium Structures which took place in Via del Mar, Chile, in December 2001. This book consists of two parts, the first one has three lectures written by Professors H.R. Brand, M. Moreau and L.S. Tuckerman. H.R. Brand gives an overview about reorientation and undulation instabilities in liquid crystals, M. Moreau presents recent results on biased tracer diffusion in lattice gases, finally, L.S. Tuckerman summarizes some numerical methods used in bifurcation problems. The second part consists of a collection of selected seminars which cover different topics in nonlinear physics, from an experimental, numerical and theoretical point of view. This book should appeal to mathematicians, physicists and engineers interested in dynamical systems, statistical mechanics, and nonequilibrium systems.
