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• W2868918247 abstract "Let $S$ be a compact, connected, oriented surface, possibly with boundary, of negative Euler characteristic. In this article we extend Lindenstrauss-Mirzakhani's and Hamenstadt's classification of locally finite mapping class group invariant ergodic measures on the space of measured laminations $mathcal{M}mathcal{L}(S)$ to the space of geodesic currents $mathcal{C}(S)$, and we discuss the homogeneous case. Moreover, we extend Lindenstrauss-Mirzakhani's classification of orbit closures to $mathcal{C}(S)$. Our argument relies on their results and on the decomposition of a current into a sum of three currents with isotopically disjoint supports: a measured lamination without closed leaves, a simple multi-curve and a current that binds its hull." @default.
• W2868918247 created "2018-07-19" @default.
• W2868918247 creator A5002071723 @default.
• W2868918247 creator A5020916399 @default.
• W2868918247 date "2018-07-05" @default.
• W2868918247 modified "2023-09-27" @default.
• W2868918247 title "Ergodic invariant measures on the space of geodesic currents" @default.
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