Further Dense Properties of the Space of Circle Diffeomorphisms with a Liouville Rotation Number

In continuation of Matsumoto’s paper (Nonlinearity 25:1495–1511, 2012 ) we show that various subspaces are C ∞ -dense in the space of orientation-preserving C ∞ -diffeomorphisms of the circle with rotation number α , where α ∈ S 1 is any prescribed Liouville number. In particular, for every odometer...

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Bibliographic Details
Published in:Journal of dynamics and differential equations 2018-09, Vol.30 (3), p.1145-1160
Main Author: Kunde, Philipp
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
Odometers
Ordinary Differential Equations
Partial Differential Equations
Rotation
Subspaces
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Summary:In continuation of Matsumoto’s paper (Nonlinearity 25:1495–1511, 2012 ) we show that various subspaces are C ∞ -dense in the space of orientation-preserving C ∞ -diffeomorphisms of the circle with rotation number α , where α ∈ S 1 is any prescribed Liouville number. In particular, for every odometer O of product type we prove the denseness of the subspace of diffeomorphisms which are orbit-equivalent to O .
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-017-9592-4