2002/10/09 by Bastien Fernandez, Fernandez, Bastien, Pierre Guiraud +1
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #nlin.CD
paper · pdf · doi:10.48550/arxiv.nlin/0210019
20 pages, 4 figures
arxiv created 2002/10/09 · arxiv updated 2009/11/30
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, approximations of the corresponding symbolic systems are obtained. These approximations imply that 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.