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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.14740 |
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| _version_ | 1866911313197793280 |
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| author | Henriksen, Christian Petersen, Carsten Lunde Uhre, Eva |
| author_facet | Henriksen, Christian Petersen, Carsten Lunde Uhre, Eva |
| contents | Let $K\subset\mathbb{C}$ be non-polar, compact and polynomially convex. We study the limits of equilibrium measures on preimages of compact sets, under $K$-regular sequences of polynomials, that center on $K$ and under the sequences of derivatives of all orders of such sequences. We show that under mild assumptions such limits always exist and equal the equilibrium measure on $K$. From this we derive convergence of the equilibrium distributions on the Julia sets of the sequence of polynomials and their derivatives of all orders. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14740 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Convergence of Equilibrium Measures under $K$-regular Polynomial Sequences and their Derivatives Henriksen, Christian Petersen, Carsten Lunde Uhre, Eva Dynamical Systems Complex Variables 31A05 (Primary) 37F10, 42C05 (Secondary) Let $K\subset\mathbb{C}$ be non-polar, compact and polynomially convex. We study the limits of equilibrium measures on preimages of compact sets, under $K$-regular sequences of polynomials, that center on $K$ and under the sequences of derivatives of all orders of such sequences. We show that under mild assumptions such limits always exist and equal the equilibrium measure on $K$. From this we derive convergence of the equilibrium distributions on the Julia sets of the sequence of polynomials and their derivatives of all orders. |
| title | Convergence of Equilibrium Measures under $K$-regular Polynomial Sequences and their Derivatives |
| topic | Dynamical Systems Complex Variables 31A05 (Primary) 37F10, 42C05 (Secondary) |
| url | https://arxiv.org/abs/2312.14740 |