Chaos, Dynamics, and Fractals : An Algorithmic Approach to Deterministic Chaos
Joseph L. McCauley
Bok Engelsk 1993 · Electronic books.
| Annen tittel | |
|---|---|
| Utgitt | Cambridge : : Cambridge University Press, , 1993.
|
| Omfang | 1 online resource (349 p.)
|
| Opplysninger | Description based upon print version of record.. - Cover; Half Title; Title Page; Copyright; Dedication; Contents; Preface; Introduction; 1 Flows in phase space; 1.1 Determinism, phase flows, and Liouville's theorem; 1.2 Equilibria, linear stability, and limit cycles; 1.3 Change of stability (bifurcations); 1.4 Periodically driven systems and stroboscopic maps; 1.5 Continuous groups of transformations as phase space flows; 2 Introduction to deterministic chaos; 2.1 The Lorenz model, the Lorenz plot, and the binary tent map; 2.2 Local exponential instability of nearby orbits: the positiveLiapunov exponent. - 2.3 The Frobenius-Peron equation (invariant densities)2.4 Simple examples of fully developed chaos for maps of theinterval; 2.5 Maps that are conjugate under differentiable coordinatetransformations; 2.6 Computation of nonperiodic chaotic orbits at fullydeveloped chaos; 2.7 Is the idea of randomness necessary in natural science?; 3 Conservative dynamical systems; 3.1 Integrable conservative systems: symmetry, invariance, conservation laws, and motion on invariant tori in phase space; 3.2 The Hénon-Heiles model: evidence for bifurcations from integrable to chaotic behavior. - 3.3 Perturbed twist maps: nearly integrable conservativesystems3.4 Mixing and ergodicity: the approach to statisticalequilibrium; 3.5 The bakers' transformation; 3.6 Computation of chaotic orbits for an area-preserving map; Appendix 3.A Generating functions for canonicaltransformations; Appendix 3.B Systems in involution; 4 Fractals and fragmentation in phase space; 4.1 Introduction to fractals; 4.2 Geometrically selfsimilar fractals; 4.3 The dissipative bakers' transformation: a model 'strange' attractor; 4.4 The symmetric tent map: a model 'strange' repeller. - 4.5 The devil's staircase: arithmetic on the Cantor set4.6 Generalized dimensions and the coarsegraining of phasespace; 4.7 Computation of chaotic orbits on a fractal; 5 The way to chaos by instability of quasiperiodic orbits; 5.1 From limit cycles to tori to chaos; 5.2 Periodically driven systems and circle maps; 5.3 Arnol'd tongues and the devil's staircase; 5.4 Scaling laws and renormalization group equations; 5.5 The Farey tree; 6 The way to chaos by period doubling; 6.1 Universality at transitions to chaos; 6.2 Instability of periodic orbits by period doubling. - 6.3 Universal scaling for noninvertible quadratic maps of theinterval7 Introduction tomultifractals; 7.1 Incomplete but optimal information: the natural coarsegraining of phase space; 7.2 The f(α)-spectrum; 7.3 The asymmetric tent map and the two-scale Cantor set (f(α) and entropy); 7.4 Multifractals at the borderlines of chaos; 8 Statistical mechanics on symbol sequences; 8.1 Introduction to statistical mechanics; 8.2 Introduction to symbolic dynamics; 8.3 The transfer matrix method; 8.4 What is the temperature of chaotic motion on a fractal?. - 8.5 [ƒ(bar)] as a thermodynamic prediction in the canonical ensemble. - The author presents deterministic chaos from the standpoint of theoretical computer arithmetic, leading to universal properties described by symbolic dynamics.
|
| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 0521416582. - 0521467470
|
