Expansion properties of Double Standard Maps

2020/02/05 by Benedicks, Michael, Misiurewicz, Michal, Rodrigues, Ana · 1 citation
#37Dxx #37Exx #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.02019

Abstract

For the family of Double Standard Maps f_a,b=2x+a+\fracbπ sin2πx \pmod1 we investigate the structure of the space of parameters a when b=1 and when b∈[0,1). In the first case the maps have a critical point, but for a set of parameters E₁ of positive Lebesgue measure there is an invariant absolutely continuous measure for f_a,1. In the second case there is an open nonempty set E_b of parameters for which the map f_a,b is expanding. We show that as b\nearrow 1, the set E_b accumulates on many points of E₁ in a regular way from the measure point of view.

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• Uniformization of tongues in Double Standard Map family and variation of maximal chaotic sets

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