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This book looks at dynamics as an iteration process where the output of a function is fed back as an input to determine the evolution of an initial state over time. The theory examines errors which arise from round-off in numerical simulations, from the inexactness of mathematical models used to describe physical processes, and from the effects of external controls. The author provides an introduction accessible to beginning graduate students and emphasizing geometric aspects of the theory. Conley's ideas about rough orbits and chain-recurrence play a central role in the treatment. The book wi

Differentiable dynamical systems. --- Iterative methods (Mathematics) --- Iteration (Mathematics) --- Numerical analysis --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Dynamique différentiable --- Itération (Mathématiques)

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Operator theory --- Differentiable dynamical systems --- Flows (Differentiable dynamical systems) --- Hyperbolic spaces --- Invariant manifolds --- Invariants --- Manifolds (Mathematics) --- Hyperbolic complex manifolds --- Manifolds, Hyperbolic complex --- Spaces, Hyperbolic --- Geometry, Non-Euclidean --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Differentiable dynamical systems. --- Systèmes dynamiques. --- Hyperbolic spaces. --- Espaces hyperboliques. --- Invariant manifolds. --- Variétés invariantes. --- Flows (Differentiable dynamical systems).

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Nonlinear theories --- Chaotic behavior in systems --- Differentiable dynamical systems --- Chaotic behavior in systems. --- Differentiable dynamical systems. --- Nonlinear theories. --- Nonlinear problems --- Nonlinearity (Mathematics) --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Calculus --- Mathematical analysis --- Mathematical physics --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Dynamics --- System theory --- Théories non linéaires --- Chaos --- Dynamique différentiable

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Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modem as well as the classical techniques of applied mathematics. This renewal of interest,both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The developmentof new courses is a natural consequenceof a high level of excite­ ment on the research frontier as newer techniques, such as numerical and symbolic computersystems,dynamicalsystems,and chaos, mix with and reinforce the tradi­ tional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbookssuitable for use in advancedundergraduate and begin­ ning graduate courses, and will complement the Applied Mathematical Seiences (AMS) series, which will focus on advanced textbooks and research level mono­ graphs. Preface Tbe purpose of this preface is twofold. Firstly, to give an informal historical in­ troduction to the subject area of this book, Systems and Control , and secondly, to explain the philosophy of the approach to this subject taken in this book and to outline the topics that will be covered.

Differentiable dynamical systems --- Control theory --- 519.71 --- 519.72 --- #TELE:SISTA --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Dynamics --- Machine theory --- Control systems theory: mathematical aspects --- Information theory: mathematical aspects --- 519.72 Information theory: mathematical aspects --- 519.71 Control systems theory: mathematical aspects --- Dynamique différentiable --- Commande, Théorie de la --- Calculus of variations. --- Chemometrics. --- Computational intelligence. --- Calculus of Variations and Optimal Control; Optimization. --- Math. Applications in Chemistry. --- Computational Intelligence. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Chemistry, Analytic --- Analytical chemistry --- Chemistry --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Mathematics --- Measurement --- Statistical methods --- Differentiable dynamical systems. --- Systèmes, Théorie des --- Commande, Théorie de la --- Dynamique différentiable --- Systèmes, Théorie des