Non degenerate Birkhoff functions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914894222196736 |
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| author | Garay, Mauricio van Straten, Duco |
| author_facet | Garay, Mauricio van Straten, Duco |
| contents | It is known after the works of Mahler, Kleinbock, Margulis, Sprindžuk and others that very well approximated numbers on a manifold form a zero measure set, assuming non-degeneracy conditions. These non-degeneracy conditions are, in many applications, difficult to check. We propose here a setting in which these are automatic. Rather than functions, we consider correspondences which have a better behaviour. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21495 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non degenerate Birkhoff functions Garay, Mauricio van Straten, Duco Dynamical Systems Number Theory 11J83 37J40 It is known after the works of Mahler, Kleinbock, Margulis, Sprindžuk and others that very well approximated numbers on a manifold form a zero measure set, assuming non-degeneracy conditions. These non-degeneracy conditions are, in many applications, difficult to check. We propose here a setting in which these are automatic. Rather than functions, we consider correspondences which have a better behaviour. |
| title | Non degenerate Birkhoff functions |
| topic | Dynamical Systems Number Theory 11J83 37J40 |
| url | https://arxiv.org/abs/2407.21495 |