dc.contributor Guàrdia Munarriz, Marcel dc.contributor Martín de la Torre, Pablo dc.contributor.author Granell i Yuste, Francesc dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtiques dc.date.accessioned 2016-09-08T10:55:41Z dc.date.available 2016-09-08T10:55:41Z dc.date.issued 2016-07 dc.identifier.uri http://hdl.handle.net/2117/89735 dc.description.abstract This thesis gives an introduction to the theory of quasiconformal surgery. To that end, we consider the complexification of the Arnol'd standard family of circle maps. These functions are analytically linearisable under certain conditions, and therefore have a Herman ring $\wtilde U_\ve$ (where $\ve$ is a parameter of the map) around the unit circle, whose size $\wtilde R_\ve$ tends to infinity as $\ve$ tends to zero. We study the asymptotic size of these Herman rings and check that \wtilde R_\ve=\frac{2}{\ve}(R_0+\cO(\ve\log\ve)), where $R_0$ is the conformal radius of the Siegel disc of the complex semistandard map. In order to achieve this, we perform a quasiconformal surgery construction to relate $\wtilde F_{\alpha(\ve),\ve}$ and $G$, and hyperbolic geometry to obtain the quantitative result. dc.language.iso eng dc.publisher Universitat Politècnica de Catalunya dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics dc.subject.lcsh Differentiable dynamical systems dc.subject.other Quasiconformal surgery dc.subject.other Riemann Mapping Theorem dc.subject.other Poincaré metric dc.subject.other Analytically linearisable dc.subject.other Brjuno number dc.subject.other Herman ring dc.subject.other Arnol'd standard family dc.title Asymptotic size of Herman Rings using quasiconformal surgery dc.type Bachelor thesis dc.subject.lemac Sistemes dinàmics diferenciables dc.subject.ams Classificació AMS::37 Dynamical systems and ergodic theory::37F Complex dynamical systems dc.identifier.slug FME-1334 dc.rights.access Open Access dc.date.updated 2016-07-23T05:43:13Z dc.audience.educationlevel Grau dc.audience.mediator Universitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística
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