03995nam 2200601Ia 450 991087677050332120200520144314.01-280-52105-897866105210503-527-60480-43-527-60641-6(CKB)1000000000377376(EBL)481669(OCoLC)69245285(SSID)ssj0000137618(PQKBManifestationID)11141838(PQKBTitleCode)TC0000137618(PQKBWorkID)10097057(PQKB)10928710(MiAaPQ)EBC481669(EXLCZ)99100000000037737620030318d2005 uy 0engur|n|---|||||txtccrDeterministic chaos an introduction /Heinz Georg Schuster and Wolfram Just4th rev. and enl. ed.Weinheim ;[Great Britain] Wiley-VCHc20051 online resource (315 p.)Previous ed.: 1995.3-527-40415-5 Includes bibliographical references and index.Deterministic Chaos An Introduction; Contents; Preface; Legends to Plates I-XX; 1 Introduction; 2 Experiments and Simple Models; 2.1 Experimental Detection of Deterministic Chaos; 2.1.1 Driven Pendulum; 2.1.2 Rayleigh-Bénard System in a Box; 2.1.3 Stirred Chemical Reactions; 2.1.4 Hénon-Heiles System; 2.2 The Periodically Kicked Rotator; 2.2.1 Logistic Map; 2.2.2 Hénon Map; 2.2.3 Chirikov Map; 3 Piecewise Linear Maps and Deterministic Chaos; 3.1 The Bernoulli Shift; 3.2 Characterization of Chaotic Motion; 3.2.1 Liapunov Exponent; 3.2.2 Invariant Measure; 3.2.3 Correlation Function6 Strange Attractors in Dissipative Dynamical Systems6.1 Introduction and Definition of Strange Attractors; 6.1.1 Baker's Transformation; 6.1.2 Dissipative Hénon Map; 6.2 The Kolmogorov Entropy; 6.2.1 Definition of K; 6.2.2 Connection of K to the Liapunov Exponents; 6.2.3 Average Time over which the State of a Chaotic System can be Predicted; 6.3 Characterization of the Attractor by a Measured Signal; 6.3.1 Reconstruction of the Attractor from a Time Series; 6.3.2 Generalized Dimensions and Distribution of Singularities in the Invariant Density6.3.3 Generalized Entropies and Fluctuations around the K-Entropy6.3.4 Kaplan-Yorke Conjecture; 6.4 Pictures of Strange Attractors and Fractal Boundaries; 7 The Transition from Quasiperiodicity to Chaos; 7.1 Strange Attractors and the Onset of Turbulence; 7.1.1 Hopf Bifurcation; 7.1.2 Landau's Route to Turbulence; 7.1.3 Ruelle-Takens-Newhouse Route to Chaos; 7.1.4 Possibility of Three-Frequency Quasiperiodic Orbits; 7.1.5 Break-up of a Two-Torus; 7.2 Universal Properties of the Transition from Quasiperiodicity to Chaos; 7.2.1 Mode Locking and the Farey Tree; 7.2.2 Local Universality7.2.3 Global UniversalityA new edition of this well-established monograph, this volume provides a comprehensive overview over the still fascinating field of chaos research. The authors include recent developments such as systems with restricted degrees of freedom but put also a strong emphasis on the mathematical foundations. Partly illustrated in color, this fourth edition features new sections from applied nonlinear science, like control of chaos, synchronisation of nonlinear systems, and turbulence, as well as recent theoretical concepts like strange nonchaotic attractors, on-off intermittency and spatio-temporal cStatistical physicsDeterministic chaosStatistical physics.Deterministic chaos.530.1Schuster Heinz Georg1943-48625Just W(Wolfram)958198MiAaPQMiAaPQMiAaPQBOOK9910876770503321Deterministic chaos4188497UNINA