Séminaire de géométrie, groupes et dynamiques - Unité de mathématiques pures et appliquées - UMPA/ENSL - Lyon - Sud-Est
Unité de mathématiques pures et appliquées - UMPA/ENSL - Lyon - Sud-Est
Natalia Goncharuk: "Complex rotation numbers and renormalization ": *annulé*
Start:
Dec. 15, 2021, 2 p.m.
End:
Dec. 15, 2021, 3 p.m.
Speaker:
Title:
Natalia Goncharuk: "Complex rotation numbers and renormalization ": *annulé*
Abstract: <div class="v1moz-forward-container">
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<div>Given an analytic circle diffeomorphism $f$ and a complex number $\omega\in \bbH$, consider a fundamental domain of $f+\omega$ in $\bbC/\bbZ$ that is close to $\bbR/\bbZ$. The quotient space of this fundamental domain via $f+\omega$ is a torus. The<span> </span><strong>complex rotation number</strong> of $f+\omega$ equals the modulus of this torus. This construction is due to V. Arnold (1978).</div>
<div>As $\omega\to 0$, the limit values of the complex rotation number form an approximately self-similar set ``bubbles''.</div>
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I will give a survey of results on complex rotation numbers and bubbles, discuss a new hyperbolicity result for the renormalization of analytic diffeomorphisms $f\colon \bbR/\bbZ \to \bbC/\bbZ$ (joint work with M. Yampolsky) and the implications of this new result to the geometry of bubbles (joint work with I. Gorbovickis).</div>
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Loc. UMPA
Cat. Séminaires
ref:
Séminaire de géométrie, groupes et dynamiques - Unité de mathématiques pures et appliquées - UMPA/ENSL - Lyon - Sud-Est