par Basios, Vasileios 
;Forti, GIAN LUIGI ;Gilbert, Thomas
Référence Journal of Physics A: Mathematical and Theoretical, 42, 3, page (035102)
Publication Publié, 2009
;Forti, GIAN LUIGI ;Gilbert, Thomas Référence Journal of Physics A: Mathematical and Theoretical, 42, 3, page (035102)
Publication Publié, 2009
Article révisé par les pairs
| Résumé : | 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. factorizes 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 these 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. © 2009 IOP Publishing Ltd. |
