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

Jean-Baptiste Bardet·Gerhard Keller
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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.

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Jean-Baptiste Bardet, Gerhard Keller. 2006-05-18. Phase transitions in a piecewise expanding coupled map lattice with linear nearest neighbour coupling. https://doi.org/10.1088/0951-7715%2F19%2F9%2F012

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