Phase transitions in a piecewise expanding coupled map lattice with linear nearest neighbour coupling
Dynamical Systems
2007-09-10 v1 Probability
Abstract
We construct a mixing continuous piecewise linear map on [-1,1] with the property that a two-dimensional lattice made of these maps with a linear north and east nearest neighbour coupling admits a phase transition. We also provide a modification of this construction where the local map is an expanding analytic circle map. The basic strategy is borroughed from [Gielis-MacKay (2000)], namely we compare the dynamics of the CML to those of a probabilistic cellular automaton of Toom's type.
Cite
@article{arxiv.math/0605501,
title = {Phase transitions in a piecewise expanding coupled map lattice with linear nearest neighbour coupling},
author = {Jean-Baptiste Bardet and Gerhard Keller},
journal= {arXiv preprint arXiv:math/0605501},
year = {2007}
}
Comments
19 pages