no. 1
Ergodic invariant measures for actions of SL(2, Z)
Annales de l'institut Henri Poincaré. Section B. Calcul des probabilités et statistiques, Tome 15 (1979) no. 1, pp. 79-84. 
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     author = {Dani, S. G. and Keane, M.},
     title = {Ergodic invariant measures for actions of {SL(2,} {Z)}},
     journal = {Annales de l'institut Henri Poincar\'e. Section B. Calcul des probabilit\'es et statistiques},
     pages = {79--84},
     publisher = {Gauthier-Villars},
     volume = {15},
     number = {1},
     year = {1979},
     mrnumber = {527316},
     zbl = {0392.28018},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_1979__15_1_79_0/}
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Dani, S. G.; Keane, M. Ergodic invariant measures for actions of SL(2, Z). Annales de l'institut Henri Poincaré. Section B. Calcul des probabilités et statistiques, Tome 15 (1979) no. 1, pp. 79-84. http://archive.numdam.org/item/AIHPB_1979__15_1_79_0/

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[2] H. Furstenberg, The unique ergodicity of the horocycle flow, Recent Advances in Topological Dynamics. Lecture Notes in Math., t. 318, Springer Verlag, Berlin. | MR | Zbl

[3] K. Schmidt, Invariant measures on the circle. Preprint, Warwick.