LEADER 05456nam 2200685Ia 450 001 9910780723103321 005 20230725041500.0 010 $a1-282-75833-0 010 $a9786612758331 010 $a981-4277-66-5 035 $a(CKB)2490000000001653 035 $a(EBL)1679519 035 $a(OCoLC)741539753 035 $a(SSID)ssj0000413808 035 $a(PQKBManifestationID)11287450 035 $a(PQKBTitleCode)TC0000413808 035 $a(PQKBWorkID)10385711 035 $a(PQKB)11503159 035 $a(MiAaPQ)EBC1679519 035 $a(WSP)00000569 035 $a(Au-PeEL)EBL1679519 035 $a(CaPaEBR)ebr10422181 035 $a(CaONFJC)MIL275833 035 $a(EXLCZ)992490000000001653 100 $a20090402d2010 uy 0 101 0 $aeng 135 $aurcuu|||uu||| 181 $ctxt 182 $cc 183 $acr 200 10$aChaos$b[electronic resource] $efrom simple models to complex systems /$fMassimo Cencini, Fabio Cecconi, Angelo Vulpiani 210 $aHackensack, N.J. $cWorld Scientific$dc2010 215 $a1 online resource (482 p.) 225 1 $aSeries on advances in statistical mechanics ;$vv. 17 300 $aDescription based upon print version of record. 311 $a981-4277-65-7 320 $aIncludes bibliographical references and index. 327 $aContents; Preface; Introduction; Historical note; Overview of the book; Hints on how to use/read this book; Introduction to Dynamical Systems and Chaos; 1. First Encounter with Chaos; 1.1 Prologue; 1.2 The nonlinear pendulum; 1.3 The damped nonlinear pendulum; 1.4 The vertically driven and damped nonlinear pendulum; 1.5 What about the predictability of pendulum evolution?; 1.6 Epilogue; 2. The Language of Dynamical Systems; 2.1 Ordinary Differential Equations (ODE); 2.1.1 Conservative and dissipative dynamical systems; BoxB. 1 Hamiltonian dynamics 327 $aA: Symplectic structure and Canonical Transformations B: Integrable systems and Action-Angle variables; 2.1.2 Poincare?Map; 2.2 Discrete time dynamical systems: maps; 2.2.1 Two dimensional maps; 2.2.1.1 The He?non Map; 2.2.1.2 Two-dimensional symplectic maps; 2.3 The role of dimension; 2.4 Stability theory; 2.4.1 Classification of fixed points and linear stability analysis; BoxB. 2 A remark on the linear stability of symplectic maps; 2.4.2 Nonlinear stability; 2.4.2.1 Limit cycles; 2.4.2.2 Lyapunov Theorem; 2.5 Exercises; 3. Examples of Chaotic Behaviors; 3.1 The logisticmap 327 $aBoxB. 3 Topological conjugacy 3.2 The Lorenzmodel; BoxB. 4 Derivation of the Lorenz model; 3.3 The He?non-Heiles system; 3.4 What did we learn and what will we learn?; BoxB. 5 Correlation functions; 3.5 Closing remark; 3.6 Exercises; 4. Probabilistic Approach to Chaos; 4.1 An informal probabilistic approach; 4.2 Time evolution of the probability density; BoxB. 6 Markov Processes; A: Finite states Markov Chains; B: Continuous Markov processes; C: Dynamical systems with additive noise; 4.3 Ergodicity; 4.3.1 An historical interlude on ergodic theory; BoxB. 7 Poincare? recurrence theorem 327 $a4.3.2 Abstract formulation of the Ergodic theory 4.4 Mixing; 4.5 Markov chains and chaoticmaps; 4.6 Natural measure; 4.7 Exercises; 5. Characterization of Chaotic Dynamical Systems; 5.1 Strange attractors; 5.2 Fractals and multifractals; 5.2.1 Box counting dimension; 5.2.2 The stretching and folding mechanism; 5.2.3 Multifractals; BoxB. 8 Brief excursion on Large Deviation Theory; 5.2.4 Grassberger-Procaccia algorithm; 5.3 Characteristic Lyapunov exponents; BoxB. 9 Algorithm for computing Lyapunov Spectrum; 5.3.1 Oseledec theorem and the law of large numbers 327 $a5.3.2 Remarks on the Lyapunov exponents 5.3.2.1 Lyapunov exponents are topological invariant; 5.3.2.2 Relationship between Lyapunov exponents of flows and Poincare? maps; 5.3.3 Fluctuation statistics of finite time Lyapunov exponents; 5.3.4 Lyapunov dimension; BoxB. 10 Mathematical chaos; A: Hyperbolic sets and Anosov systems; B: SRB measure; C: The Arnold cat map; 5.4 Exercises; 6. From Order to Chaos in Dissipative Systems; 6.1 The scenarios for the transition to turbulence; 6.1.1 Landau-Hopf; BoxB. 11 Hopf bifurcation; BoxB. 12 The Van der Pol oscillator and the averaging technique 327 $a6.1.2 Ruelle-Takens 330 $aChaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information 410 0$aSeries on advances in statistical mechanics ;$vv. 17. 606 $aChaotic behavior in systems 606 $aDynamics 615 0$aChaotic behavior in systems. 615 0$aDynamics. 676 $a515.39 700 $aCencini$b Massimo$0633803 701 $aCecconi$b Fabio$0633804 701 $aVulpiani$b A$01519823 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910780723103321 996 $aChaos$93758114 997 $aUNINA