Upper bounds for the entropy in the cusp for one-parameter diagonal flows on $SL_{d}(\mathbb{R})/SL_{d}(\mathbb{Z})$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866908536070471680 |
|---|---|
| author | Mor, Ron |
| author_facet | Mor, Ron |
| contents | We give explicit upper bounds for the entropy in the cusp for one-parameter diagonal flows on $SL_d(\mathbb{R})/SL_{d}(\mathbb{Z})$. These results include bounds for the entropy of the cusp as a whole, as well as for the cusp regions corresponding to either the maximal parabolic subgroups of $SL_{d}$, or the minimal (Borel) parabolic subgroup. To do so, we use a method which involves choosing an auxiliary linear functional on the Lie algebra of the Cartan group, specifically tailored to each of the bounds we are interested in. In a follow-up paper we prove that the upper bounds we obtain in this work are tight. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01665 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Upper bounds for the entropy in the cusp for one-parameter diagonal flows on $SL_{d}(\mathbb{R})/SL_{d}(\mathbb{Z})$ Mor, Ron Dynamical Systems We give explicit upper bounds for the entropy in the cusp for one-parameter diagonal flows on $SL_d(\mathbb{R})/SL_{d}(\mathbb{Z})$. These results include bounds for the entropy of the cusp as a whole, as well as for the cusp regions corresponding to either the maximal parabolic subgroups of $SL_{d}$, or the minimal (Borel) parabolic subgroup. To do so, we use a method which involves choosing an auxiliary linear functional on the Lie algebra of the Cartan group, specifically tailored to each of the bounds we are interested in. In a follow-up paper we prove that the upper bounds we obtain in this work are tight. |
| title | Upper bounds for the entropy in the cusp for one-parameter diagonal flows on $SL_{d}(\mathbb{R})/SL_{d}(\mathbb{Z})$ |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2309.01665 |