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Multicritical circle maps and invariant distributions

Grant number: 21/04599-0
Support type:Scholarships in Brazil - Master
Effective date (Start): August 01, 2021
Effective date (End): July 31, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Edson de Faria
Grantee:Bruno de Almeida Nussenzveig
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Associated research grant:16/25053-8 - Dynamics and geometry in low dimensions, AP.TEM

Abstract

In recent years, there have been important advances in the study of cohomological equations and invariant distributions for discrete (1) and continuous (2) dynamical systems. In (1), the authors have shown that, for any minimal smooth circle diffeomorphism, the space of invariant distributions is one-dimensional, generated by the invariant probability measure. Our main goal with the current project is to attempt a characterization of the space of invariant distributions in the case of multicritical circle maps. (1) Artur Avila and Alejandro Kocsard, Cohomological equations and invariant distributions for minimal circle diffeomorphisms, Duke Math. J. 158 (2011), no. 3, 501-536. (2) Livio Flaminio, Giovanni Forni, and Federico Rodriguez Hertz, Invariant distributions for homogeneous flows and affine transformations, J. Mod. Dyn. 10 (2016), 33-79. (AU)

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