Lyapunov modes in extended systems

被引:8
|
作者
Yang, Hong-Liu [1 ]
Radons, Guenter [1 ]
机构
[1] Tech Univ Chemnitz, Inst Phys, D-09107 Chemnitz, Germany
关键词
Lyapunov modes; hyperbolicity; branch splitting; effective degrees of freedom; DISK FLUIDS; EXPONENTS; DYNAMICS;
D O I
10.1098/rsta.2009.0067
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
Hydrodynamic Lyapunov modes, which have recently been observed in many extended systems with translational symmetry, such as hard sphere systems, dynamic XY models or Lennard-Jones fluids, are nowadays regarded as fundamental objects connecting nonlinear dynamics and statistical physics. We review here our recent results on Lyapunov modes in extended system. The solution to one of the puzzles, the appearance of good and 'vague' modes, is presented for the model system of coupled map lattices. The structural properties of these modes are related to the phase space geometry, especially the angles between Oseledec subspaces, and to fluctuations of local Lyapunov exponents. In this context, we report also on the possible appearance of branches splitting in the Lyapunov spectra of diatomic systems, similar to acoustic and optical branches for phonons. The final part is devoted to the hyperbolicity of partial differential equations and the effective degrees of freedom of such in finite-dimensional systems.
引用
收藏
页码:3197 / 3212
页数:16
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