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

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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.
19 pages

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Dynamical Systems, Probability, 37L40 37L60 82C20

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http://salesiana.dossiersoluciones.com/handle/123456789/137558

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0605501
 http://arxiv.org/abs/math/0605501
 Nonlinearity 19 (2006) 2193-2210
 doi:10.1088/0951-7715/19/9/012

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arXiv