Exceptional Sets in Dynamical Systems and Diophantine Approximation

Maurice Dodson ()
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Maurice Dodson: University of York, Department of Mathematics

A chapter in Rigidity in Dynamics and Geometry, 2002, pp 77-98 from Springer

Abstract: Abstract The nature and origin of exceptional sets associated with the rotation number of circle maps, Kolmogorov-Arnol’d-Moser theory on the existence of invariant tori and the linearisation of complex diffeomorphisms are explained. The metrical properties of these exceptional sets are closely related to fundamental results in the metrical theory of Diophantine approximation. The counterpart of Diophantine approximation in hyperbolic space and a dynamical interpretation which led to the very general notion of’ shrinking targets’ are sketched and the recent use of flows in homogeneous spaces of lattices in the proof of the Baker-Sprindzuk conjecture is described briefly.

Keywords: Homogeneous Space; Hyperbolic Space; Hausdorff Dimension; Rotation Number; Diophantine Approximation (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-04743-9_4

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DOI: 10.1007/978-3-662-04743-9_4

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