Topology Proceedings 28 No. 2 (2004), pp. 617-637

Rhythmic functions and IP recurrence

Randall McCutcheon

Various classes of functions arising in the study of a problem in Diophantine approximation are studied. Chief among these are so-called rhythmic functions, as defined analytically by J. van der Corput, and IP recurrent functions, as defined analytically by H. Furstenberg and B. Weiss. Equivalent definitions for these classes are given in the language of topological dynamics, and strong parallels are observed in consequence. A recently developed alternative method for attacking the underlying Diophantine approximation problem is mentioned, with new results thereby obtained.

Keywords: Minimality, distality, rhythmicity, IP recurrence, syndeticity, VIP systems, Diophantine approximation

Mathematics Subject Classification: 11J25 (37B20)

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Topology Proceedings, Volume 28, No. 2 (2004)
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