Ergodic Measures in Strata

2025/08/22 by Bestvina, Mladen, Chaika, Jon, Hensel, Sebastian
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2508.16215

Abstract

We determine the number of ergodic measures in each stratum of geodesic laminations on a surface.

Citations

• Nonunique Ergodicity on the Boundary of Outer space
• Generic measures for translation surface flows
• The number of ergodic measures for transitive subshifts under the regular bispecial condition
• There exists an interval exchange with a non-ergodic generic measure
• Almost filling laminations and the connectivity of ending lamination space

Related

• Ergodic invariant measures on the space of geodesic currents
• Limit sets of Teichm "uller geodesics with minimal non-uniquely ergodic\n vertical foliation
• Unique Ergodicity of Translation Flows
• Measured geodesic laminations in Flatland
• Invariant measures on the space of measured laminations for subgroups of mapping class group