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37F25, Renormalization — 3 results found.

      
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KAM-renormalization and Herman Rings for 2D Maps
C. R. Math. Rep. Acad. Sci. Canada Vol. 43 (2) 2021, pp. 78-86
Michael Yampolsky (Received: 2021/03/14, Revised: 2021/04/21)

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In this note, we extend the renormalization horseshoe we have recently constructed with N. Goncharuk for analytic diffeomorphisms of the circle to their small two-dimensional perturbations. As one consequence, Herman rings with rotation numbers of bounded type survive on a codimension one set of parameters under small two-dimensional perturbations.

On étend le fer à cheval de renormalisation récemment construit avec N. Goncharuk pour les difféomorphismes analytiques du cercle à leurs petites perturbations à deux dimensions. Il suit que les anneaux de Herman à nombre de rotation de type borné survivent sur un ensemble de paramètres à codimension un sous petites perturbations à deux dimensions.

Renormalization of Bi-cubic Circle Maps
C. R. Math. Rep. Acad. Sci. Canada Vol. 41 (4) 2019, pp. 57-83
Michael Yampolsky (Received: 2019/09/03, Revised: 2019/12/19)

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We develop a renormalization theory for analytic homeomorphisms of the circle with two cubic critical points. We prove a renormalization hyperbolicity theorem. As a basis for the proofs, we develop complex a priori bounds for multi-critical circle maps.

On développe une théorie de renormalisation pour les homéomorphismes analytiques du cercle à deux points critiques cubiques. On démontre un théorème d’hyperbolicité dans le cadre de renormalisation. Comme base des démonstrations, on développe des bornes complexes a priori pour les applications du cercle dans lui-même aux points critiques multiples

Renormalization of Unicritical Analytic Circle Maps
C. R. Math. Rep. Acad. Sci. Canada Vol. 39 (3) 2017, pp. 77-89
Michael Yampolsky (Received: 2016/09/26, Revised: 2016/12/23)

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In this paper we generalize renormalization theory for analytic critical circle maps with a cubic critical point to the case of maps with an arbitrary odd critical exponent by proving a quasiconformal rigidity statement for renormalizations of such maps.

Dans cet article on généralise la théorie de la renormalisation pour les transformations criticales analytiques du circle à point critical cubique au cas de transformations à exposant critical impair arbitraire, en démontrant une affirmation de rigidité quasi-conforme.

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algebraic number theory approximation property automorphisms Bessel functions Boson-fermion correspondence C*-algebra Carmichael number center problem Chebyshev transform classification Classification of simple C*-algebras composition operators continued fractions Cuntz Semigroup elliptic curves fixed point Fourier transform function fields. functoriality general relativity generic property ideals indefinite inner product inductive limits of sub-homogeneous C*- algebras Irrational rotation algebra J-Hermitian matrix K-theory Kahler manifolds L-functions maximal ideal space nonexpansive mapping numerical range orthogonal polynomials Predual space prime number property SP Renormalization rotation algebras Salem number semi-reciprocal polynomials tracially approximate splitting interval algebras unbounded traces uniqueness Weak Markov set Whitney problems

Most used AMS

05C05 11A07 11A55 11B37 11B68 11D09 11D25 11D41 11E04 11F11 11F66 11F67 11G05 11R09 11R11 13B25 14J26 14M25 14P10 17B37 17B67 19K14 19K56 26A51 30C15 30H05 35B 37E10 37E20 37F25 39B72 42C05 43A07 46B20 46L05 46L35 46L40 46L55 46L80 47H10 53B25 53C55 54C60 60F10 83C05

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