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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.