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Route to chaotic synchronisation in coupled map lattices: Rigorous results

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  • Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an admissibility condition, upper and lower bounds of the corresponding symbolic systems are obtained. As a consequence, the topological entropy is located between two decreasing step functions of the coupling parameter. The analysis firstly applies to mappings with piecewise affine local maps which allow explicit expressions and, in a second step, is extended by continuity to mappings with piecewise smooth local maps.
    Mathematics Subject Classification: 37D20, 37E99, 37B10.


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