A variational principle for holomorphic correspondences
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914368124354560 |
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| author | Gopinathan, Subith Sridharan, Shrihari |
| author_facet | Gopinathan, Subith Sridharan, Shrihari |
| contents | In this paper, we consider a dynamical system on the Riemann sphere that evolves through a set-valued map, namely a holomorphic correspondence. Analogous to the investigation of the dynamics effected by a continuous map defined on a compact metric space, wherein the concept of measure-theoretic entropy of the map and its utility in defining the pressure of a function are well-studied, we define the measure-theoretic entropy of a holomorphic correspondence and use the same to define the pressure of continuous functions. These ideas naturally lead to the formulation of a variational principle in the context of the dynamics of a holomorphic correspondence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03786 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A variational principle for holomorphic correspondences Gopinathan, Subith Sridharan, Shrihari Dynamical Systems 37D35, 37A35, 37F05 In this paper, we consider a dynamical system on the Riemann sphere that evolves through a set-valued map, namely a holomorphic correspondence. Analogous to the investigation of the dynamics effected by a continuous map defined on a compact metric space, wherein the concept of measure-theoretic entropy of the map and its utility in defining the pressure of a function are well-studied, we define the measure-theoretic entropy of a holomorphic correspondence and use the same to define the pressure of continuous functions. These ideas naturally lead to the formulation of a variational principle in the context of the dynamics of a holomorphic correspondence. |
| title | A variational principle for holomorphic correspondences |
| topic | Dynamical Systems 37D35, 37A35, 37F05 |
| url | https://arxiv.org/abs/2603.03786 |