Phase transitions in a piecewise expanding coupled map lattice with linear nearest neighbour coupling

Details Phase transitions in a piecewise expanding coupled map lattice with linear nearest neighbour coupling Phase transitions in a piecewise expanding coupled map lattice with linear nearest neighbour coupling

2006-05-18

arxiv.org/abs/math/0605501v1

Nonlinearity 19 (2006) 2193-2210

Mathematics

Dynamical Systems

19 pages

Scientific paper

10.1088/0951-7715/19/9/012

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.

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