Large intersection properties in Diophantine approximation and dynamical systems

Abstract

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.

24 pages

References in corpus (2)

• A lecture on the classical KAM theorem
• Random wavelet series based on a tree-indexed Markov chain

Cited by in corpus (3)

• Diophantine approximations, large intersections and geodesics in negative curvature
• Some remarks on Mahler's classification in higher dimension
• Describability via ubiquity and eutaxy in Diophantine approximation