Logarithm Laws for Unipotent Flows, II
Jayadev S. Athreya, Gregory Margulis
TL;DR
This paper establishes logarithm laws for unipotent flows on homogeneous spaces, extending previous results and exploring connections with multi-dimensional Diophantine approximation.
Contribution
It provides new analogs of Sullivan and Kleinbock-Margulis logarithm laws specifically for unipotent flows on homogeneous spaces.
Findings
Proved logarithm laws for horospherical actions on homogeneous spaces.
Established relations between unipotent flows and multi-dimensional Diophantine approximation.
Abstract
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 homogeneous spaces . We describe some relations with multi-dimensional diophantine approximation.
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Taxonomy
TopicsMathematical Dynamics and Fractals · advanced mathematical theories · Algebraic Geometry and Number Theory