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Journal Articles Nonlinearity Year : 2022

Smooth generalized interval exchange transformations with wandering intervals, from explicit derived from pseudo-Anosov maps

Abstract

Abstract Starting from any pseudo-Anosov map ϕ on a surface of genus g ⩾ 2 , we construct explicitly a family of Derived from pseudo-Anosov maps f by adapting the construction of Smale’s derived from Anosov maps on the two-torus. This is done by perturbing ϕ at some fixed points. We first consider perturbations at every conical fixed point and then at regular fixed points. We establish the existence of a measure µ , supported by the non-trivial unique minimal component of the stable foliation of f , with respect to which f is mixing. In the process, we construct a uniquely ergodic generalized interval exchange transformation (GIET) with a wandering interval that is semi-conjugated to a self-similar interval exchange transformation. This GIET is obtained as the Poincaré map of a flow renormalized by f which parametrizes stable foliation. When f is , the flow and the GIET are .

Dates and versions

hal-03906886 , version 1 (19-12-2022)

Identifiers

Cite

Jérôme Carrand. Smooth generalized interval exchange transformations with wandering intervals, from explicit derived from pseudo-Anosov maps. Nonlinearity, 2022, 36 (1), pp.476-506. ⟨10.1088/1361-6544/aca5e0⟩. ⟨hal-03906886⟩
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