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dc.contributorGuàrdia Munarriz, Marcel
dc.contributorMartín de la Torre, Pablo
dc.contributor.authorGranell i Yuste, Francesc
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.description.abstractThis 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.publisherUniversitat Politècnica de Catalunya
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics
dc.subject.lcshDifferentiable dynamical systems
dc.subject.otherQuasiconformal surgery
dc.subject.otherRiemann Mapping Theorem
dc.subject.otherPoincaré metric
dc.subject.otherAnalytically linearisable
dc.subject.otherBrjuno number
dc.subject.otherHerman ring
dc.subject.otherArnol'd standard family
dc.titleAsymptotic size of Herman Rings using quasiconformal surgery
dc.typeBachelor thesis
dc.subject.lemacSistemes dinàmics diferenciables
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37F Complex dynamical systems
dc.rights.accessOpen Access
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística

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