Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Perturbations of countable Markov maps

Sara Munday

created by daniele on 09 Jan 2016

13 jan 2016 -- 11:00

Sala Conferenze, Collegio Puteano, CRM, Pisa

Seminari di Sistemi Dinamici Olomorfi, Pisa

Abstract.

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We investigate how the dynamics of a countable Markov map change when the map is perturbed by analysing the topological conjugacy maps between the original and perturbed system. These conjugacies are strictly increasing singular maps (i.e., with derivative Lebesgue-almost-everywhere equal to zero). We can show that under certain conditions, the Hausdorff dimension of the set of points where the derivative is nonzero is continuous, in the sense that as the perturbation is made smaller and smaller, the dimension tends to 1. On the other hand, for various other quantities (including Hoelder exponent) we give simple examples to show.

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