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math.DS2014
Logarithm Laws for Unipotent Flows, II
Jayadev S. Athreya, Gregory Margulis
We prove analogs of the logarithm laws of Sullivan and Kleinbock-Margulis in the context of unipotent flows. In particular, we prove results for horospherical actions on homogeneou…
math.DS2014★ 6 cited
Spherical averages of Siegel transforms for higher rank diagonal actions and applications
Jayadev S. Athreya, Anish Ghosh, Jimmy Tseng
We investigate the geometry of approximates in multiplicative Diophantine approximation. Our main tool is a new multiparameter averaging result for Siegel transforms on the space o…
math.DS2012
Logarithm laws for strong unstable foliations in negative curvature and non-Archimedian Diophantine approximation
Jayadev S. Athreya, Frédéric Paulin
Given for instance a finite volume negatively curved Riemannian manifold , we give a precise relation between the logarithmic growth rates of the excursions into cusps neighborh…