2020/02/04 by Florent Ygouf, Ygouf, Florent
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2002.01186
openalex publication_date 2020/02/04 · openalex created_date 2022/11/15 · openalex updated_date 2026/07/28
We define on any affine invariant orbifold M a foliation FM that generalises the isoperiodic foliation on strata of the moduli space of translation surfaces and study the dynamics of its leaves in the rank 1 case. We establish a criterion that ensures the density of the leaves and provide two applications of this criterion. The first one is a classification of the dynamical behavior of the leaves of FM when M is Prym eigenform locus in genus 3 and the second provides the first examples of dense isoperiodic leaves in the stratum H(2, 1, 1).