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DC Field | Value | Language |
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dc.contributor.author | Fagella Rabionet, Núria | - |
dc.contributor.author | Martínez-Seara Alonso, M. Teresa | - |
dc.contributor.author | Villanueva Castelltort, Jordi | - |
dc.date.accessioned | 2020-06-05T06:34:18Z | - |
dc.date.available | 2020-06-05T06:34:18Z | - |
dc.date.issued | 2004-05 | - |
dc.identifier.issn | 0143-3857 | - |
dc.identifier.uri | http://hdl.handle.net/2445/164370 | - |
dc.description.abstract | In this paper we consider the complexification of the Arnold standard family of circle maps given by $\widetilde F_{\alpha,\epsilon}(u)=ue^{i\alpha} e^{({\epsilon}/{2}) (u-{1}/{u})}$, with $\alpha=\alpha(\epsilon)$ chosen so that $\widetilde F_{\alpha(\epsilon),\epsilon}$ restricted to the unit circle has a prefixed rotation number $\theta$ belonging to the set of Brjuno numbers. In this case, it is known that $\widetilde F_{\alpha(\epsilon),\epsilon}$ is analytically linearizable if $\epsilon$ is small enough and so it has a Herman ring $\widetilde U_{\epsilon}$ around the unit circle. Using Yoccoz's estimates, one has that the size$\widetilde R_\epsilon$ of $\widetilde U_{\epsilon}$ (so that $\widetilde U_{\epsilon}$ is conformally equivalent to $\{u\in{\mathbb C}: 1/\widetilde R_\epsilon < |u| < \widetilde R_\epsilon\}$) goes to infinity as $\epsilon\to 0$, but one may ask for its asymptotic behavior. We prove that $\widetilde R_\epsilon=({2}/{\epsilon})(R_0+\mathcal{O}(\epsilon\log\epsilon))$, where R0 is the conformal radius of the Siegel disk of the complex semistandard map $G(z)=ze^{i\omega}e^z$, where $\omega= 2\pi\theta$. In the proof we use a very explicit quasiconformal surgery construction to relate $\widetilde F_{\alpha(\epsilon),\epsilon}$ and G, and hyperbolic geometry to obtain the quantitative result. | - |
dc.format.extent | 32 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Cambridge University Press | - |
dc.relation.isformatof | Reproducció del document publicat a: https://doi.org/10.1017/S0143385704000045 | - |
dc.relation.ispartof | Ergodic Theory and Dynamical Systems, 2004, vol. 24, num. 3, p. 735-766 | - |
dc.relation.uri | https://doi.org/10.1017/S0143385704000045 | - |
dc.rights | (c) Cambridge University Press, 2004 | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Sistemes dinàmics complexos | - |
dc.subject.classification | Teoria geomètrica de funcions | - |
dc.subject.classification | Superfícies de Riemann | - |
dc.subject.other | Complex dynamical systems | - |
dc.subject.other | Geometric function theory | - |
dc.subject.other | Riemann surfaces | - |
dc.title | Asymptotic size of Herman rings of the complex standard family by quantitative quasiconformal surgery | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/publishedVersion | - |
dc.identifier.idgrec | 550478 | - |
dc.date.updated | 2020-06-05T06:34:19Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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File | Description | Size | Format | |
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550478.pdf | 351.95 kB | Adobe PDF | View/Open |
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