Positive entropy invariant measures on the space of lattices with escape of mass
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Kadyrov, Shirali
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On the space of unimodular lattices, we construct a sequence of invariant probability measures under a singular diagonal element with high entropy and show that the limit measure is 0
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Kadyrov, S. (2012). Positive entropy invariant measures on the space of lattices with escape of mass. Ergodic Theory and Dynamical Systems, 32(1), 141-157.