Statistical properties of time-reversible triangular maps of the square

Details Statistical properties of time-reversible triangular maps of the square Statistical properties of time-reversible triangular maps of the square

2008-12-09

arxiv.org/abs/0812.1648v1

J. Phys. A: Math. Theor. 42 (2009) 035102

Nonlinear Sciences

Chaotic Dynamics

15 pages, 3 figures

Scientific paper

10.1088/1751-8113/42/3/035102

Time reversal symmetric triangular maps of the unit square are introduced with the property that the time evolution of one of their two variables is determined by a piecewise expanding map of the unit interval. We study their statistical properties and establish the conditions under which their equilibrium measures have a product structure, i.e. factorises in a symmetric form. When these conditions are not verified, the equilibrium measure does not have a product form and therefore provides additional information on the statistical properties of theses maps. This is the case of anti-symmetric cusp maps, which have an intermittent fixed point and yet have uniform invariant measures on the unit interval. We construct the invariant density of the corresponding two-dimensional triangular map and prove that it exhibits a singularity at the intermittent fixed point.

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