• Circle diffeomorphisms: quasi-...

Result: Circle diffeomorphisms: quasi-reducibility and commuting diffeomorphisms

Title:
Circle diffeomorphisms: quasi-reducibility and commuting diffeomorphisms
Authors:
BENHENDA, Mostapha
Source:
Nonlinearity (Bristol. Print). 25(7):1981-1995
Publisher Information:
Bristol: Institute of Physics, 2012.
Publication Year:
2012
Physical Description:
print, 10 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Variétés et complexes cellulaires, Manifolds and cell complexes, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Analyse non linéaire, Nonlinear analysis, análisis no lineal, Cercle, Circle, Circulo, Difféomorphisme, Diffeomorphism, Difeomorfism, Physique mathématique, Mathematical physics, Física matemática, Rotation, Rotación, Réductibilité, Reducibility, Reductibilidad, 57R50, 58D05, Nombre irrationnel, Nombre rotation
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
Laboratoire d'Analyse, Geometrie et Applications, Paris 13 University, 99 Avenue J B Clement, 93430 Villetaneuse, France
ISSN:
0951-7715
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=26131760
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics

Theoretical physics
Accession Number:
edscal.26131760
Database:
PASCAL Archive

Further Information

In this paper, we show two related results on circle diffeomorphisms. The first result is on quasi-reducibility: for a Baire-dense set of α, for any diffeomorphism f of rotation number α, it is possible to accumulate Rα with a sequence hn f h―1n, hn being a diffeomorphism. The second result is: for a Baire-dense set of α, given two commuting diffeomorphisms f and g, such that f has α for rotation number, it is possible to approach each of them by commuting diffeomorphisms fn and gn that are differentiably conjugated to rotations. In particular, it implies that if α is in this Baire-dense set, and if β is an irrational number such that (α, β) are not simultaneously Diophantine, then the set of commuting diffeomorphisms (f, g) with singular conjugacy, and with rotation numbers (α, β), respectively, is C∞-dense in the set of commuting diffeomorphisms with rotation numbers (α, β).