Two-step equidistribution for bi-quadratic torus packets

Ilya Khayutin (Northwestern University)

02-Dec-2021, 17:15-18:30 (2 years ago)

Abstract: A major challenge to the asymptotic analysis of a sequence of probability measures on a homogeneous space, invariant under diagonalizable groups, is the possibility of accumulation on intermediate homogeneous subspaces. In this aspect higher rank homogeneous flows cannot be expected to share the rigidity properties of unipotent ones. In particular, the linearization technique fails for diagonalizable flows.

In a joint work in progress with A. Wieser we show how in favorable situations one can actually use the existence of intermediate homogeneous spaces in our benefit. We show that periodic measures on some packets of periodic torus orbits on PGL4(Z)\PGL4(R) converge in the limit to a measure with a non-trivial Haar component. The proof goes by establishing high entropy for the limit measure. The method utilizes the intermediate homogeneous space to split the analysis into two more tractable steps.

dynamical systemsnumber theory

Audience: general audience


New England Dynamics and Number Theory Seminar

Organizers: Dmitry Kleinbock, Han Li*, Lam Pham, Felipe Ramirez
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