Titlebook: Dynamics of Circle Mappings; Edson de Faria,Pablo Guarino Textbook 2024Latest edition The Editor(s) (if applicable) and The Author(s), und

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Quasisymmetric RigidityIn addition to the real bounds, another important preliminary step towards establishing the . of multicritical circle maps (to be examined in Sect. .) is to answer the question: When are two topologically conjugate multicritical circle maps . conjugate? This question pertains to the general study of . of one-dimensional systems.

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Ergodic AspectsIn this chapter we examine multicritical circle maps from the point of view of measurable dynamics. We have seen in Theorem . that every homeomorphism of the circle without periodic points is uniquely ergodic. In particular, every multicritical circle map . with irrational rotation number is uniquely ergodic.

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Quasiconformal DeformationsThis chapter should be regarded as a second intermezzo (after Chap. .). Here we briefly review some standard facts about the theory of quasiconformal mappings in the complex plane and the Riemann sphere. In such a short exposition we can hardly do justice to this beautiful and powerful theory.

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Renormalization: Holomorphic MethodsIn this final chapter we will survey some of the complex-analytic ideas that play a decisive role in the theory of (multi)critical circle maps.

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