Analytical Approach for Piecewise Linear Coupled Map Lattices

Details Analytical Approach for Piecewise Linear Coupled Map Lattices Analytical Approach for Piecewise Linear Coupled Map Lattices

1997-11-13

arxiv.org/abs/chao-dyn/9711014v1

Nonlinear Sciences

Chaotic Dynamics

22 pages Latex, 8 figures, also avaiable at http://athene.fkp.physik.th-darmstadt.de/public/wolfram.html

Scientific paper

10.1023/A:1023272819435

A simple construction is presented, which generalises piecewise linear one-dimensional Markov maps to an arbitrary number of dimensions. The corresponding coupled map lattice, known as a simplicial mapping in the mathematical literature, allows for an analytical investigation. Especially the spin Hamiltonian, which is generated by the symbolic dynamics is accessible. As an example a formal relation between a globally coupled system and an Ising mean field model is established. The phase transition in the limit of infinite system size is analysed and analytical results are compared with numerical simulations.

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