Pressure path metrics on parabolic families of polynomials
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914950149046272 |
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| author | Bianchi, Fabrizio He, Yan Mary |
| author_facet | Bianchi, Fabrizio He, Yan Mary |
| contents | Let $Λ$ be a subfamily of the moduli space of degree $D\ge2$ polynomials defined by a finite number of parabolic relations. Let $Ω$ be a bounded stable component of $Λ$ with the property that all critical points are attracted by either the persistent parabolic cycles or by attracting cycles in $\mathbb C$. We construct a positive semi-definite pressure form on $Ω$ and show that it defines a path metric on $Ω$. This provides a counterpart in complex dynamics of the pressure metric on cusped Hitchin components recently studied by Kao and Bray-Canary-Kao-Martone. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10462 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pressure path metrics on parabolic families of polynomials Bianchi, Fabrizio He, Yan Mary Dynamical Systems Complex Variables Geometric Topology Let $Λ$ be a subfamily of the moduli space of degree $D\ge2$ polynomials defined by a finite number of parabolic relations. Let $Ω$ be a bounded stable component of $Λ$ with the property that all critical points are attracted by either the persistent parabolic cycles or by attracting cycles in $\mathbb C$. We construct a positive semi-definite pressure form on $Ω$ and show that it defines a path metric on $Ω$. This provides a counterpart in complex dynamics of the pressure metric on cusped Hitchin components recently studied by Kao and Bray-Canary-Kao-Martone. |
| title | Pressure path metrics on parabolic families of polynomials |
| topic | Dynamical Systems Complex Variables Geometric Topology |
| url | https://arxiv.org/abs/2409.10462 |