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The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics. It has greatly stimulated research in many sciences and given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introduction for senior undergraduate and beginning graduate students of mathematics, physics, and engineering combines mathematical rigor with copious examples of important applications. It covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. Readers need not be familiar with manifolds or measure theory; the only prerequisite is a basic undergraduate analysis course. The authors begin by describing the wide array of scientific and mathematical questions that dynamics can address. They then use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. The final chapters introduce modern developments and applications of dynamics. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory.

Differential geometry. Global analysis --- Differentiable dynamical systems. --- Dynamique différentiable --- 531.3 --- Dynamics. Kinetics --- 531.3 Dynamics. Kinetics --- Dynamique différentiable --- Differentiable dynamical systems --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics

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This volume is intended for advanced undergraduate or first-year graduate students as an introduction to applied nonlinear dynamics and chaos. The author has placed emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about the behavior of these systems. He has included the basic core material that is necessary for higher levels of study and research. Thus, people who do not necessarily have an extensive mathematical background, such as students in engineering, physics, chemistry, and biology, will find this text as useful as students of mathematics. This new edition contains extensive new material on invariant manifold theory and normal forms (in particular, Hamiltonian normal forms and the role of symmetry). Lagrangian, Hamiltonian, gradient, and reversible dynamical systems are also discussed. Elementary Hamiltonian bifurcations are covered, as well as the basic properties of circle maps. The book contains an extensive bibliography as well as a detailed glossary of terms, making it a comprehensive book on applied nonlinear dynamical systems from a geometrical and analytical point of view.

Differentiable dynamical systems --- Nonlinear theories --- Chaotic behavior in systems --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- 517.987 --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical analysis --- Mathematical physics --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Dynamics --- System theory --- 517.987 Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Differentiable dynamical systems. --- Nonlinear theories. --- Chaotic behavior in systems. --- Dynamique différentiable --- Théories non linéaires --- Chaos --- EPUB-LIV-FT SPRINGER-B --- Mathematics. --- Dynamics. --- Ergodic theory. --- Applied mathematics. --- Engineering mathematics. --- Statistical physics. --- Dynamical systems. --- Dynamical Systems and Ergodic Theory. --- Applications of Mathematics. --- Statistical Physics, Dynamical Systems and Complexity. --- Appl.Mathematics/Computational Methods of Engineering. --- Complex Systems. --- Mathematical and Computational Engineering. --- Statistical Physics and Dynamical Systems. --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Mathematical statistics --- Engineering --- Engineering analysis --- Ergodic transformations --- Continuous groups --- Measure theory --- Transformations (Mathematics) --- Statistical methods --- System theory. --- Mathematical physics. --- Dynamical Systems. --- Mathematical and Computational Engineering Applications. --- Theoretical, Mathematical and Computational Physics. --- Data processing.