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Journal of Dynamics and Differential Equations

, Volume 30, Issue 3, pp 1145–1160 | Cite as

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

  • Philipp Kunde
Article

Abstract

In continuation of Matsumoto’s paper (Nonlinearity 25:1495–1511, 2012) we show that various subspaces are \(C^{\infty }\)-dense in the space of orientation-preserving \(C^{\infty }\)-diffeomorphisms of the circle with rotation number \(\alpha \), where \(\alpha \in {\mathbb {S}}^1\) is any prescribed Liouville number. In particular, for every odometer \({\mathcal {O}}\) of product type we prove the denseness of the subspace of diffeomorphisms which are orbit-equivalent to \({\mathcal {O}}\).

Keywords

Circle diffeomorphisms Orbit equivalence Rotation number Approximation by conjugation-method Odometer 

Mathematics Subject Classification

Primary 37E10 Secondary 37A20 37C05 37E45 

Notes

Acknowledgements

The author would like to thank the referee for careful proofreading and helpful comments.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of HamburgHamburgGermany

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