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Analytic linearization of conformal maps of the annulus.
- Source :
-
Advances in Mathematics . Nov2022:Part A, Vol. 409, pN.PAG-N.PAG. 1p. - Publication Year :
- 2022
-
Abstract
- We consider holomorphic maps defined in an annulus around R / Z in C / Z. E. Risler proved that in a generic analytic family of such maps f ζ that contains a Brjuno rotation f 0 (z) = z + α , all maps that are conjugate to this rotation form a codimension-1 analytic submanifold near f 0. In this paper, we obtain the Risler's result as a corollary of the following construction. We introduce a renormalization operator on the space of univalent maps in a neighborhood of R / Z. We prove that this operator is hyperbolic, with one unstable direction corresponding to translations. We further use a holomorphic motions argument and Yoccoz's theorem to show that its stable foliation consists of diffeomorphisms that are conjugate to rotations. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00018708
- Volume :
- 409
- Database :
- Academic Search Index
- Journal :
- Advances in Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 159496770
- Full Text :
- https://doi.org/10.1016/j.aim.2022.108636