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Journal of the London Mathematical Society Advance Access originally published online on January 21, 2009
Journal of the London Mathematical Society 2009 79(2):377-398; doi:10.1112/jlms/jdn077
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© 2009 London Mathematical Society

Large intersection properties in Diophantine approximation and dynamical systems

Arnaud Durand

Applied and Computational Mathematics
California Institute of Technology
1200 E. California Blvd. – MC 217-50
Pasadena, CA 91125
USA
Current address:
Université Paris-Sud 11
Mathématiques – Bât. 425
91405 Orsay Cedex, France
arnaud.durand@math.u-psud.fr

We investigate the large intersection properties of the set of points that are approximated at a certain rate by a family of affine subspaces. We then apply our results to various sets arising in the metric theory of Diophantine approximation, in the study of the homeomorphisms of the circle, and in the perturbation theory for Hamiltonian systems.

2000 Mathematics Subject Classification 28A80 (primary), 11J83, 28A78, 37E10, 37J40 (secondary).

Received March 27, 2008; revised October 9, 2008; published online January 21, 2009.


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