The Limit Points of Weyl Sums and Other Continuous Cocycles
نویسنده
چکیده
This paper examines the limit points of continuous Z-cocycles defined on a minimal dynamical system and taking values in an abelian metrisable group. This is motivated by and applied to the study of classical exponential series X^-i^"'" 6+nx) t 0 show, in particular, that if 0 is a transcendental number with liminfe^ ||^|| < oo, then for each x chosen from a dense Gd subset of [0,1], these partial sums are dense in C. Indeed the associated cocycle is topologically transitive. Several generalisations to higher degree polynomials and higher dimensions are presented.
منابع مشابه
2 2 N ov 2 00 5 2 - Cocycles of the Lie superalgebras of Weyl type
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