On measures invariant under diagonalizable actions: the Rank-One case and the general Low-Entropy method
Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus OH 43210-1174, United States
Fine Hall, Washington Road, Princeton NJ 08544-1000, United States
This rigidity theorem, which is a generalized and more conceptual form of the low entropy method of [14,3] is used to classify positive entropy measures invariant under a one parameter group with an additional recurrence condition for $G=G_1 \times G_2$ with $G_1$ a rank one algebraic group. Further applications of this rigidity statement will appear in forthcoming papers.
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