02948nam 22005893 450 991096305220332120231110230443.097814704728491470472848(MiAaPQ)EBC30222589(Au-PeEL)EBL30222589(CKB)25289779400041(OCoLC)1350689740(EXLCZ)992528977940004120221110d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierHorocycle Dynamics1st ed.Providence :American Mathematical Society,2022.©2022.1 online resource (112 pages)Memoirs of the American Mathematical Society ;v.280Print version: Bainbridge, Matthew Horocycle Dynamics: New Invariants and Eigenform Loci in the Stratum Providence : American Mathematical Society,c2022 9781470455392 "We study dynamics of the horocycle flow on strata of translation surfaces, introduce new invariants for ergodic measures, and analyze the interaction of the horocycle flow and real Rel surgeries. We use this analysis to complete and extend results of Calta and Wortman classifying horocycle-invariant measures in the eigenform loci. In addition we classify the horocycle orbit-closures and prove that every orbit is equidistributed in its orbit-closure. We also prove equidistribution results describing limits of sequences of measures. Our results have applications to the problem of counting closed trajectories on translation surfaces of genus 2"--Provided by publisher.Memoirs of the American Mathematical Society Topological dynamicsErgodic theoryRandom dynamical systemsDynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior -- Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)mscFunctions of a complex variable -- Riemann surfaces -- Differentials on Riemann surfacesmscTopological dynamics.Ergodic theory.Random dynamical systems.Dynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior -- Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.).Functions of a complex variable -- Riemann surfaces -- Differentials on Riemann surfaces.515/.39515.3937D4030F30mscBainbridge Matthew1801334Smillie John1801335Weiss Barak1801336MiAaPQMiAaPQMiAaPQBOOK9910963052203321Horocycle Dynamics4346492UNINA