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Differential geometry. Global analysis --- Differentiable dynamical systems --- Differentieerbare dynamicasystemen --- Systèmes dynamiques différentiables --- Differential equations, Nonlinear --- Differentiable dynamical systems. --- Numerical Solutions. --- 51 --- -Nonlinear differential equations --- Nonlinear theories --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Mathematics --- Numerical solutions --- -Mathematics --- 51 Mathematics --- -Differential dynamical systems --- Nonlinear differential equations --- Numerical analysis --- Numerical Solutions --- Differential equations [Nonlinear ] --- Differential equations, Nonlinear - Numerical Solutions.

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Differential geometry. Global analysis --- Chaotic behavior in systems --- Differentiable dynamical systems --- Transport theory --- Chaos --- Dynamique différentiable --- Transport, Théorie du --- Differentiable dynamical systems. --- Transport theory. --- Chaotic behavior in systems. --- Chaos in systems --- Chaotic motion in systems --- Chaotisch gedrag in de systemen --- Comportement chaotique dans les systèmes --- Differential dynamical systems --- Théorie du transport --- Transporttheorie --- Dynamique différentiable --- Transport, Théorie du

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Mathematical control systems --- Ordinary differential equations --- Differentiable dynamical systems --- Lyapunov exponents --- Stochastic systems --- Dynamique différentiable --- Systèmes stochastiques --- Congresses --- Congrès --- Congresses. --- 51 --- -Lyapunov exponents --- -Stochastic systems --- -Systems, Stochastic --- Stochastic processes --- System analysis --- Liapunov exponents --- Lyapunov characteristic exponents --- Differential equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- Mathematics --- -Mathematics --- 51 Mathematics --- -51 Mathematics --- Systems, Stochastic --- Dynamique différentiable --- Systèmes stochastiques --- Congrès --- Stochastic systems - Congresses. --- Lyapunov exponents - Congresses. --- Differentiable dynamical systems - Congresses.

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This book is an introduction to the theory of shadowing of approximate trajectories in dynamical systems by exact ones. This is the first book completely devoted to the theory of shadowing. It shows the importance of shadowing theory for both the qualitative theory of dynamical systems and the theory of numerical methods. Shadowing Methods allow us to estimate differences between exact and approximate solutions on infinite time intervals and to understand the influence of error terms. The book is intended for specialists in dynamical systems, for researchers and graduate students in the theory of numerical methods.

Shadowing (Differentiable dynamical systems) --- Differential equations --- Geometry --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Numerical solutions --- Shadowing (Differentieerbare dynamische systemen) --- Shadowing (Systèmes dynamiques différentiables) --- 517.91 --- 517.91 Differential equations --- Shadowing theorem --- Theorem, Shadowing --- Differentiable dynamical systems --- Numerical solutions. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Dynamics. --- Ergodic theory. --- Global Analysis and Analysis on Manifolds. --- Dynamical Systems and Ergodic Theory. --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Numerical solutions&delete& --- Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics

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From the 18th to the 30th August 2003 , a NATO Advanced Study Institute (ASI) was held in Cargèse, Corsica, France. Cargèse is a nice small village situated by the mediterranean sea and the Institut d'Etudes Scientifiques de Cargese provides ? a traditional place to organize Theoretical Physics Summer Schools and Workshops * in a closed and well equiped place. The ASI was an International Summer School on "Chaotic Dynamics and Transport in Classical and Quantum Systems". The main goal of the school was to develop the mutual interaction between Physics and Mathematics concerning statistical properties of classical and quantum dynamical systems. Various experimental and numerical observations have shown new phenomena of chaotic and anomalous transport, fractal structures, chaos in physics accelerators and in cooled atoms inside atom-optics billiards, space-time chaos, fluctuations far from equilibrium, quantum decoherence etc. New theoretical methods have been developed in order to modelize and to understand these phenomena (volume preserving and ergodic dynamical systems, non-equilibrium statistical dynamics, fractional kinetics, coupled maps, space-time entropy, quantum dissipative processes etc). The school gathered a team of specialists from several horizons lecturing and discussing on the achievements, perspectives and open problems (both fundamental and applied).

Chaotic behavior in systems --- Quantum theory --- Chaos --- Congresses. --- Congrès --- EPUB-LIV-FT LIVPHYSI SPRINGER-B --- Congresses --- Physics. --- Differentiable dynamical systems. --- Statistical physics. --- Physics, general. --- Dynamical Systems and Ergodic Theory. --- Complex Systems. --- Classical and Continuum Physics. --- Statistical Physics and Dynamical Systems. --- Physics --- Mathematical statistics --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Statistical methods --- Dynamics. --- Ergodic theory. --- Dynamical systems. --- Continuum physics. --- Classical field theory --- Continuum physics --- Continuum mechanics --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Chaotic dynamics