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100			_aWiggins, Stephen. _920481
245			_aIntroduction to Applied Nonlinear Dynamical Systems and Chaos _h[electronic resource] / _cby Stephen Wiggins.
250			_a2nd ed. 2003.
260			_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2003.
300			_aXXXVIII, 844 p. _bonline resource.
505			_aEquilibrium Solutions, Stability, and Linearized Stability -- Liapunov Functions -- Invariant Manifolds: Linear and Nonlinear Systems -- Periodic Orbits -- Vector Fields Possessing an Integral -- Index Theory -- Some General Properties of Vector Fields: Existence, Uniqueness, Differentiability, and Flows -- Asymptotic Behavior -- The Poincaré-Bendixson Theorem -- Poincaré Maps -- Conjugacies of Maps, and Varying the Cross-Section -- Structural Stability, Genericity, and Transversality -- Lagrange's Equations -- Hamiltonian Vector Fields -- Gradient Vector Fields -- Reversible Dynamical Systems -- Asymptotically Autonomous Vector Fields -- Center Manifolds -- Normal Forms -- Bifurcation of Fixed Points of Vector Fields -- Bifurcations of Fixed Points of Maps -- On the Interpretation and Application of Bifurcation Diagrams: A Word of Caution -- The Smale Horseshoe -- Symbolic Dynamics -- The Conley-Moser Conditions, or "How to Prove That a Dynamical System is Chaotic" -- Dynamics Near Homoclinic Points of Two-Dimensional Maps -- Orbits Homoclinic to Hyperbolic Fixed Points in Three-Dimensional Autonomous Vector Fields -- Melnikov-s Method for Homoclinic Orbits in Two-Dimensional, Time-Periodic Vector Fields -- Liapunov Exponents -- Chaos and Strange Attractors -- Hyperbolic Invariant Sets: A Chaotic Saddle -- Long Period Sinks in Dissipative Systems and Elliptic Islands in Conservative Systems -- Global Bifurcations Arising from Local Codimension-Two Bifurcations -- Glossary of Frequently Used Terms.
520			_aThis 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.
650			_aDynamical systems. _920482
650			_aMathematics. _920483
650			_aSystem theory. _920484
650			_aEngineering mathematics. _920485
650			_aEngineering-Data processing. _920486
650			_aMathematical physics. _920487
650			_aDynamical Systems. _920488
650			_aApplications of Mathematics. _920489
650			_aComplex Systems. _920490
650			_aMathematical and Computational Engineering Applications. _920491
650			_aTheoretical, Mathematical and Computational Physics. _920492
856			_uhttps://doi.org/10.1007/b97481
942			_cEBK
999			_c13645 _d13645