Bounding entropy for one-parameter diagonal flows on $SL_{d}(\mathbb{R})/SL_{d}(\mathbb{Z})$ using linear functionals
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913180889907200 |
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| author | Mor, Ron |
| author_facet | Mor, Ron |
| contents | We give a method to bound the entropy of measures on $SL_{d}(\mathbb{R})/SL_{d}(\mathbb{Z})$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_07122 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bounding entropy for one-parameter diagonal flows on $SL_{d}(\mathbb{R})/SL_{d}(\mathbb{Z})$ using linear functionals Mor, Ron Dynamical Systems We give a method to bound the entropy of measures on $SL_{d}(\mathbb{R})/SL_{d}(\mathbb{Z})$ 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. |
| title | Bounding entropy for one-parameter diagonal flows on $SL_{d}(\mathbb{R})/SL_{d}(\mathbb{Z})$ using linear functionals |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2302.07122 |