Dynamics of some dissipative gap maps [ Back ]

Date:
24.02.14   
Times:
15:30 to 16:30
Place:
CRM - Auditori (C1/034)
Speaker:
Márcio Ricardo Alves Gouveia
University:
Universidade Estadual Paulista (UNESP)

Abstract:

Motivated by return maps near saddles for three-dimensional flows and also by return maps in the torus associated to Cherry flows, we study gap maps with derivative positive and smaller than one outside the discontinuity point. We prove that the lamination of infinitely renormalizable maps has analytic leaves in a natural subset of a Banach space of analytic maps of this kind. With maps having Hölder continuous derivative and derivative bounded away from zero, we also prove Hölder continuity of holonomies of the lamination and also of conjugacies between maps having the same combinatorics.