Gibbsian Distribution on the Lorenz Attractor

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概要

• 論文の詳細を見る

• A representation of the Lorentz attractor by a 1-dimensional Ising system is constructed. Gibbsian distribution function which describes the irregular motion of this dissipative dynamical system is investigated with the help of this representation. Relation between measure-theoretical entropy and positive Lyapunov characteristic exponent is also investigated. The following conclusions are obtained: (1) The statistical properties of the Lorenz system can be reduced to those of 1-dimensional Ising system with short-range interaction, in other words, the time correlation function of the Lorenz system shows no singular long-time behaviour. (2) The positive Lyapunov characteristic exponent of the Lorenz system is almost equal to its measure-theoretical entropy.

• 理論物理学刊行会の論文
• 1979-07-25

著者

• SHIMADA Ippei

  Atomic Energy research Institute, College of Science and Technology Nihon University

• Shimada Ippei

  Department Of Physic Hokkaido University

関連論文

• Generating Function and Its Formal Derivatives for Dynamical Systems
• On the C-System-Like Property of the Lorenz System
• Optimized Statistical Model for Lorenz System : Complex Dynamics in Nonlinear Systems
• Phase Transition between Stationary State. III : An Integral Equation for Necessary and Sufficient Liapounoff Functions
• Gibbsian Distribution on the Lorenz Attractor
• Phase Transition between Stationary States. II : Liapounoff Function in Benard Problem
• The Wandering Motion on the Lorenz Surface
• The Iterative Transition Phenomenon between Periodic and Turbulent States in a Dissipative Dynamical System
• A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems

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