LEADER 02948nam 22005893 450 001 9910963052203321 005 20231110230443.0 010 $a9781470472849 010 $a1470472848 035 $a(MiAaPQ)EBC30222589 035 $a(Au-PeEL)EBL30222589 035 $a(CKB)25289779400041 035 $a(OCoLC)1350689740 035 $a(EXLCZ)9925289779400041 100 $a20221110d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHorocycle Dynamics 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2022. 210 4$dİ2022. 215 $a1 online resource (112 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.280 311 08$aPrint version: Bainbridge, Matthew Horocycle Dynamics: New Invariants and Eigenform Loci in the Stratum Providence : American Mathematical Society,c2022 9781470455392 330 $a"We study dynamics of the horocycle flow on strata of translation surfaces, introduce new invariants for ergodic measures, and analyze the interaction of the horocycle flow and real Rel surgeries. We use this analysis to complete and extend results of Calta and Wortman classifying horocycle-invariant measures in the eigenform loci. In addition we classify the horocycle orbit-closures and prove that every orbit is equidistributed in its orbit-closure. We also prove equidistribution results describing limits of sequences of measures. Our results have applications to the problem of counting closed trajectories on translation surfaces of genus 2"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aTopological dynamics 606 $aErgodic theory 606 $aRandom dynamical systems 606 $aDynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior -- Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)$2msc 606 $aFunctions of a complex variable -- Riemann surfaces -- Differentials on Riemann surfaces$2msc 615 0$aTopological dynamics. 615 0$aErgodic theory. 615 0$aRandom dynamical systems. 615 7$aDynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior -- Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.). 615 7$aFunctions of a complex variable -- Riemann surfaces -- Differentials on Riemann surfaces. 676 $a515/.39 676 $a515.39 686 $a37D40$a30F30$2msc 700 $aBainbridge$b Matthew$01801334 701 $aSmillie$b John$01801335 701 $aWeiss$b Barak$01801336 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910963052203321 996 $aHorocycle Dynamics$94346492 997 $aUNINA