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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2405.12517 |
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| _version_ | 1866914803884228608 |
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| author | Irokawa, Reimi |
| author_facet | Irokawa, Reimi |
| contents | We study degenerating families of hyperbolic dynamics over complex K3 surfaces by means of the theory of hybrid spaces by Boucksom, Favre, and Jonsson. For an analytic family of hyperbolic automorphisms $\{f_t: X_t\to X_t\}_{t\in\mathbb{D}^*}$ over K3 surfaces $X_t$ that is possibly meromorphically degenerating at the origin, we consider the family of invariant measures $\{η_t\}$ on $X_t$ constructed by Cantat. The family $f_t$ induces a hyperbolic automorphism $f_{\mathbb{C}((t))}^{\mathop{\mathrm{an}}}:X_{\mathbb{C}((t))}^{\mathop{\mathrm{an}}}\to X_{\mathbb{C}((t))}^{\mathop{\mathrm{an}}}$ over the induced non-archimedean K3 surface, where we also have a measure $η_0$ by Filip. Our main theorem states the weak convergence of $\{η_t\}$ to $η_0$ as $t\to0$ over the induced so-called hybrid space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12517 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hybrid dynamics of hyperbolic automorphisms of K3 surfaces Irokawa, Reimi Dynamical Systems Algebraic Geometry Primary: 37F10, Secondary: 14G22, 37P30, 32A08 We study degenerating families of hyperbolic dynamics over complex K3 surfaces by means of the theory of hybrid spaces by Boucksom, Favre, and Jonsson. For an analytic family of hyperbolic automorphisms $\{f_t: X_t\to X_t\}_{t\in\mathbb{D}^*}$ over K3 surfaces $X_t$ that is possibly meromorphically degenerating at the origin, we consider the family of invariant measures $\{η_t\}$ on $X_t$ constructed by Cantat. The family $f_t$ induces a hyperbolic automorphism $f_{\mathbb{C}((t))}^{\mathop{\mathrm{an}}}:X_{\mathbb{C}((t))}^{\mathop{\mathrm{an}}}\to X_{\mathbb{C}((t))}^{\mathop{\mathrm{an}}}$ over the induced non-archimedean K3 surface, where we also have a measure $η_0$ by Filip. Our main theorem states the weak convergence of $\{η_t\}$ to $η_0$ as $t\to0$ over the induced so-called hybrid space. |
| title | Hybrid dynamics of hyperbolic automorphisms of K3 surfaces |
| topic | Dynamical Systems Algebraic Geometry Primary: 37F10, Secondary: 14G22, 37P30, 32A08 |
| url | https://arxiv.org/abs/2405.12517 |