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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2211.08809 |
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| _version_ | 1866916252895674368 |
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| author | Chaubet, Yann Bonthonneau, Yannick Guedes |
| author_facet | Chaubet, Yann Bonthonneau, Yannick Guedes |
| contents | Dynamical series such as the Ruelle zeta function have become a staple in the study of hyperbolic flows. They are usually analyzed by relating them to the resolvent of the vector field. In this paper we give the general form of such relations, which involves the intersection of the kernel of said resolvent with integration currents. Our formula is actually valid for any smooth flow, not necessarily hyperbolic. As an application, we introduce certain dynamical series that had not appeared before. Finally, we compute their value at zero, and their relation with topological invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_08809 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Resolvent of vector fields and Lefschetz numbers Chaubet, Yann Bonthonneau, Yannick Guedes Dynamical Systems Differential Geometry Dynamical series such as the Ruelle zeta function have become a staple in the study of hyperbolic flows. They are usually analyzed by relating them to the resolvent of the vector field. In this paper we give the general form of such relations, which involves the intersection of the kernel of said resolvent with integration currents. Our formula is actually valid for any smooth flow, not necessarily hyperbolic. As an application, we introduce certain dynamical series that had not appeared before. Finally, we compute their value at zero, and their relation with topological invariants. |
| title | Resolvent of vector fields and Lefschetz numbers |
| topic | Dynamical Systems Differential Geometry |
| url | https://arxiv.org/abs/2211.08809 |