LEADER 03995nam 2200601Ia 450 001 9910876770503321 005 20200520144314.0 010 $a1-280-52105-8 010 $a9786610521050 010 $a3-527-60480-4 010 $a3-527-60641-6 035 $a(CKB)1000000000377376 035 $a(EBL)481669 035 $a(OCoLC)69245285 035 $a(SSID)ssj0000137618 035 $a(PQKBManifestationID)11141838 035 $a(PQKBTitleCode)TC0000137618 035 $a(PQKBWorkID)10097057 035 $a(PQKB)10928710 035 $a(MiAaPQ)EBC481669 035 $a(EXLCZ)991000000000377376 100 $a20030318d2005 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDeterministic chaos $ean introduction /$fHeinz Georg Schuster and Wolfram Just 205 $a4th rev. and enl. ed. 210 $aWeinheim ;$a[Great Britain] $cWiley-VCH$dc2005 215 $a1 online resource (315 p.) 300 $aPrevious ed.: 1995. 311 $a3-527-40415-5 320 $aIncludes bibliographical references and index. 327 $aDeterministic 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-Be?nard System in a Box; 2.1.3 Stirred Chemical Reactions; 2.1.4 He?non-Heiles System; 2.2 The Periodically Kicked Rotator; 2.2.1 Logistic Map; 2.2.2 He?non 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 Function 327 $a6 Strange Attractors in Dissipative Dynamical Systems6.1 Introduction and Definition of Strange Attractors; 6.1.1 Baker's Transformation; 6.1.2 Dissipative He?non 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 Density 327 $a6.3.3 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 Universality 327 $a7.2.3 Global Universality 330 $aA 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 c 606 $aStatistical physics 606 $aDeterministic chaos 615 0$aStatistical physics. 615 0$aDeterministic chaos. 676 $a530.1 700 $aSchuster$b Heinz Georg$f1943-$048625 701 $aJust$b W$g(Wolfram)$0958198 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910876770503321 996 $aDeterministic chaos$94188497 997 $aUNINA