The Arnold cat map, the Ulam method and time reversal

PHYSICA D-NONLINEAR PHENOMENA

卷:241

Article

Ermann, L.¹  Shepelyansky, D. L.¹ 

[1] Univ Toulouse, UPS, IRSAMC, Lab Phys Theor,CNRS, F-31062 Toulouse, France

关键词: Dynamical chaos;    Markov chains;    Statistical description;   

DOI  :  10.1016/j.physd.2011.11.012

来源: Elsevier

【 摘 要 】

We study the properties of the Arnold cat map on a torus with several periodic sections using the Ulann method. This approach generates a Markov chain with the Ulam matrix approximant. We study numerically the spectrum and eigenstates of this matrix showing their relation with the Fokker-Planck relaxation and the Kolmogorov-Sinai entropy. We show that, in the frame of the Ulam method, the time reversal property of the map is preserved only on a short Ulam time which grows only logarithmically with the matrix size. Parallels with the evolution in a regime of quantum chaos are also discussed. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free