A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems

Abstract

Based on the Lyapunov characteristic exponents, the ergodic property of dissipative dynamical systems with a few degrees of freedom is studied numerically by employing, as an example, the Lorenz system. The Lorenz system shows the spectra of (+,0,-) type concerning the 1-dimensional Lyapunov exponents, and the exponents take the same values for orbits starting from almost of all initial points on the attractor.

Keywords

Lyapunov exponentAttractorDissipative systemPhysicsErgodic theoryLorenz systemDynamical systems theoryDegrees of freedom (physics and chemistry)Statistical physicsDynamical system (definition)Lyapunov functionClassical mechanicsMathematical analysisMathematical physicsNonlinear systemMathematicsQuantum mechanics

Affiliated Institutions

Hokkaido University JP

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Publication Info

Year: 1979
Type: article
Volume: 61
Issue: 6
Pages: 1605-1616
Citations: 1026
Access: Closed

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APA Style

                            
                                    I. Shimada, 
                                
                                    Tomohiro Nagashima
                                
                            (1979). 
                            A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems. 
                            Progress of Theoretical Physics
                            , 61
                            (6)
                            , 1605-1616.
                            https://doi.org/10.1143/ptp.61.1605

Identifiers

DOI: 10.1143/ptp.61.1605