A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems

1979/06/01 by I. Shimada, T. Nagashima, Tomohiro Nagashima · 18 citations
Computer Science · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.1143/ptp.61.1605

crossref issued 1979/06/01 · crossref published 1979/06/01 · crossref published-print 1979/06/01 · openalex publication_date 1979/06/01 · crossref created 2005/12/14 · crossref deposited 2017/08/24 · openalex created_date 2025/10/10 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/30

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. This result suggests that the ergodic property for general dynamical systems not necessarily belonging to the category of the axiom-A may also be characterized in the framework of the spectra of the Lyapunov characteristic exponents.

Citations

• Deterministic Nonperiodic Flow

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