Statistical mechanics of coupled map lattices. (English) Zbl 0791.60099

Bunimovich, L. A.; Sinai, Ya. G.

Kaneko, Kunihiko (ed.), Theory and applications of coupled map lattices. Chichester: John Wiley & Sons. Nonlinear Sci. Theory Appl. 169-189 (1993).

The paper is devoted to the coupled map lattices approach to the problem of the turbulence, i.e., of the spatiotemporal chaos in the behaviour of solutions of a spatially extended dynamical system. The coupled map lattice (CML) is a new class of dynamical systems with infinitely many degrees of freedom. The paper describes some classes of the CML with a short-range diffusive coupling on the one-dimensional lattice. The main tool for the proof of the existence of the spatiotemporal chaos is a modified version of the thermodynamic formalism for these CML. The phenomenon of the appearence of coherent structures from the chaotic state is discussed in connection with transition to ordered phases.
For the entire collection see [Zbl 0777.00014].

Reviewer: V.Zagrebnov (Marseille)

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
82B26	Phase transitions (general) in equilibrium statistical mechanics
82C05	Classical dynamic and nonequilibrium statistical mechanics (general)

Keywords:

coupled map lattices approach to the problem of the turbulence; coupling; spatiotemporal chaos; appearence of coherent structures; ordered phases