Bounding entropy for one-parameter diagonal flows on $\mathrm{SL}_{\mathtt{d}}(\mathbb{R})/\mathrm{SL}_{\mathtt{d}}(\mathbb{Z})$ using linear functionals
Year: 2025
Type: article
Abstract: We give a method to bound the entropy of measures on \mathrm{SL}_{\mathtt{d}}(\mathbb{R})/\mathrm{SL}_{\mathtt{d}}(\mathbb{Z}) , which are invariant under a one-parameter diagonal subgroup, in terms of entropy contributions from the regions of the cusp corresponding to different parabolic groups. These bounds depend on an auxiliary linear functional on the Lie algebra of the Cartan group. In follow-up papers, we will show how to optimize this functional to get good bounds on the cusp entropy and prove that in many cases these bounds are sharp.
DOI: 10.4171/jems/1592
Author: Ron Mor
Institution: Hebrew University of Jerusalem
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4407548675