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This book considers the theory of 'integrable' non-linear partial differential equations. The theory was developed at first by mathematical physicists but later mathematicians, particularly from the Soviet Union, were attracted to the field. In this volume are reprinted some fundamental contributions, originally published in Russian Mathematical Surveys, from some of the leading Soviet workers. Dr George Wilson has written an introduction intended to smooth the reader's path through some of the articles.

Differential equations --- 517.938 --- Boundary value problems --- -Differential equations, Nonlinear --- -517.938 Theory of dynamic systems --- Theory of dynamic systems --- Nonlinear differential equations --- Nonlinear theories --- Boundary conditions (Differential equations) --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Addresses, essays, lectures --- Differential equations, Nonlinear --- 517.938 Theory of dynamic systems --- Dynamique différentiable

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This book provides the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbits structure. The third and fourth parts develop in depth the theories of low-dimensional dynamical systems and hyperbolic dynamical systems. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up. Scientists and engineers working in applied dynamics, nonlinear science, and chaos will also find many fresh insights in this concrete and clear presentation. It contains more than four hundred systematic exercises.

Differentiable dynamical systems. --- Dynamique différentiable. --- 517.938 --- Theory of dynamic systems --- Dynamic systems --- 517.938 Theory of dynamic systems --- Differentiable dynamical systems --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Differential geometry. Global analysis --- Dynamique différentiable --- Topological dynamics. --- Dynamique topologique. --- Systèmes dynamiques. --- Dynamique différentiable. --- Systèmes dynamiques.

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Control theory --- Mathematical optimization --- Algorithms --- 517.938 --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Dynamics --- Machine theory --- Algorism --- Algebra --- Arithmetic --- 517.938 Theory of dynamic systems --- Theory of dynamic systems --- Foundations --- Algorithms. --- Control theory. --- Mathematical optimization. --- Calculus of variations --- Calcul des variations --- Numerical analysis --- Analyse numérique --- Calculus of variations. --- Numerical analysis. --- Analyse numérique --- Theorie du controle --- Optimisation --- Controle optimal

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Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying the modern theory of dynamical systems to combinatories and number theory.Originally published in 1981.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Ergodic theory. --- Topological dynamics. --- Combinatorial number theory. --- Combinatorial analysis --- Number theory --- Dynamics, Topological --- Differentiable dynamical systems --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Combinatorial number theory --- Ergodic theory --- Topological dynamics --- 517.938 --- 519.218 --- 519.218 Special stochastic processes --- Special stochastic processes --- 517.938 Theory of dynamic systems --- Theory of dynamic systems --- Ergodic theory. Information theory --- Discrete mathematics --- Théorie ergodique. --- Dynamique topologique. --- Nombres, Théorie combinatoire des. --- Théorie ergodique. --- Nombres, Théorie combinatoire des.