Let be an -algebraic semisimple group, an algebraic -subgroup, and a lattice in . Partially answering a question posed by Hillel Furstenberg in 1972, we prove that if the action of on is minimal, then it is uniquely ergodic. Our proof uses in an essential way Marina Ratner’s classification of probability measures on invariant under unipotent elements, and the study of “tubes” in .
Soient un groupe semi-simple algébrique sur , un sous-groupe algébrique sur , et un réseau dans . Répondant partiellement à une question de Hillel Furstenberg remontant à 1972, nous prouvons que si l’action de sur est minimale alors elle est uniquement ergodique. Notre preuve repose sur la classification de Marina Ratner des mesures sur invariantes sous l’action des éléments unipotents, et l’analyse des “tubes” dans .
@article{AIF_1998__48_5_1533_0, author = {Mozes, Shahar and Weiss, Barak}, title = {Minimality and unique ergodicity for subgroup actions}, journal = {Annales de l'Institut Fourier}, pages = {1533--1541}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {48}, number = {5}, year = {1998}, doi = {10.5802/aif.1665}, zbl = {0910.43010}, mrnumber = {99j:22007}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1665/} }
TY - JOUR AU - Mozes, Shahar AU - Weiss, Barak TI - Minimality and unique ergodicity for subgroup actions JO - Annales de l'Institut Fourier PY - 1998 SP - 1533 EP - 1541 VL - 48 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1665/ DO - 10.5802/aif.1665 LA - en ID - AIF_1998__48_5_1533_0 ER -
%0 Journal Article %A Mozes, Shahar %A Weiss, Barak %T Minimality and unique ergodicity for subgroup actions %J Annales de l'Institut Fourier %D 1998 %P 1533-1541 %V 48 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1665/ %R 10.5802/aif.1665 %G en %F AIF_1998__48_5_1533_0
Mozes, Shahar; Weiss, Barak. Minimality and unique ergodicity for subgroup actions. Annales de l'Institut Fourier, Volume 48 (1998) no. 5, pp. 1533-1541. doi : 10.5802/aif.1665. https://aif.centre-mersenne.org/articles/10.5802/aif.1665/
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