Dynamical Systems and Chaos
Proceedings of the Sitges Conference on Statistical Mechanics Sitges, Barcelona/Spain September 5 - 11, 1982
Published on 1. April 1983
Book
Paperback/Softback
XIV, 298 pages
978-3-540-12276-0 (ISBN)
Description
Prologue Some ideas about strange attractors.- Chaotic dynamics in Hamiltonian systems with divided phase space.- Periodic and quasi-periodic orbits for twist maps.- Macroscopic behavior in a simple chaotic Hamiltonian system.- Quantum dynamics.- A universal transition from quasi-periodicity to Chaos - Abstract.- Self-generated diffusion and universal critical properties in chaotic systems.- Subharmonics and the transition to chaos.- Low dimensional dynamics and the period doubling scenario.- Strange attractors in fluid dynamics.- Experimental aspects of the period doubling scenario.- Entropy and smooth dynamics.- Imbedding of a one-dimensional endomorphism into a two-dimensional diffeomorphism. Implications.- Strange attractors for differential delay equations.- Stochastic perturbations of some strange attractors.- Solutions of stochastic differential equations and fractal trajectories.- Continuous bifurcation and dissipative structures associated with a soft mode recombination instability in semiconductors.- On the characterization of chaotic motions.- Complex bifurcations in a periodically forced normal form.- Topological entropy and scaling behaviour.- On the analytic structure of chaos in dynamical systems.- Type-III-intermittency in a smooth perturbation of the logistic system.- Irreversible evolution of dynamical systems.- Homoclinic and heteroclinic points in the henon map.- The simple periodic orbits in the unimodal maps.- Modulation properties in decaying processes of the correlation function in a family of t-D maps.- Relaxation times and randomness for a nonlinear classical system.- Topological entropy on rotation sequences.- The taylor-green vortex : Fully developed turbulence and transition to spatial chaos.- Anharmonic systems in external periodic fieldswith chaotic behaviour.- Renormalization of non-analytical unimodal maps.- Critical fluctuations in a thermo-chemical instability.- The second order Melnikov integral applied to detect quasi-randomness.- The Fokker-Planck equation as a dynamical system.- On integrability of quadratic area preserving mappings in the plane.- Resonances: Key elements to the understanding of non linear oscillations.- On systems passing through resonances.- The Lyapunov characteristic numbers and the number of isolating integrals in galactic models.- On the periodic orbits of the Contopoulos Hamiltonian.- Feasibility of calculating dimension and topological entropy.- Diffusions generated from dynamical systems.- Report on the driven Josephson equation.
More details
Series
Edition
1983 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
XIV, 298 p.
Dimensions
Height: 244 mm
Width: 170 mm
Thickness: 18 mm
Weight
555 gr
ISBN-13
978-3-540-12276-0 (9783540122760)
DOI
10.1007/3-540-12276-1
Schweitzer Classification
Content
Prologue Some ideas about strange attractors.- Chaotic dynamics in Hamiltonian systems with divided phase space.- Periodic and quasi-periodic orbits for twist maps.- Macroscopic behavior in a simple chaotic Hamiltonian system.- Quantum dynamics.- A universal transition from quasi-periodicity to Chaos - Abstract.- Self-generated diffusion and universal critical properties in chaotic systems.- Subharmonics and the transition to chaos.- Low dimensional dynamics and the period doubling scenario.- Strange attractors in fluid dynamics.- Experimental aspects of the period doubling scenario.- Entropy and smooth dynamics.- Imbedding of a one-dimensional endomorphism into a two-dimensional diffeomorphism. Implications.- Strange attractors for differential delay equations.- Stochastic perturbations of some strange attractors.- Solutions of stochastic differential equations and fractal trajectories.- Continuous bifurcation and dissipative structures associated with a soft mode recombination instability in semiconductors.- On the characterization of chaotic motions.- Complex bifurcations in a periodically forced normal form.- Topological entropy and scaling behaviour.- On the analytic structure of chaos in dynamical systems.- Type-III-intermittency in a smooth perturbation of the logistic system.- Irreversible evolution of dynamical systems.- Homoclinic and heteroclinic points in the henon map.- The simple periodic orbits in the unimodal maps.- Modulation properties in decaying processes of the correlation function in a family of t-D maps.- Relaxation times and randomness for a nonlinear classical system.- Topological entropy on rotation sequences.- The taylor-green vortex : Fully developed turbulence and transition to spatial chaos.- Anharmonic systems in external periodic fieldswith chaotic behaviour.- Renormalization of non-analytical unimodal maps.- Critical fluctuations in a thermo-chemical instability.- The second order Melnikov integral applied to detect quasi-randomness.- The Fokker-Planck equation as a dynamical system.- On integrability of quadratic area preserving mappings in the plane.- Resonances: Key elements to the understanding of non linear oscillations.- On systems passing through resonances.- The Lyapunov characteristic numbers and the number of isolating integrals in galactic models.- On the periodic orbits of the Contopoulos Hamiltonian.- Feasibility of calculating dimension and topological entropy.- Diffusions generated from dynamical systems.- Report on the driven Josephson equation.