Ergodic Group Rotations,Hartman Setsand Kronecker Sequences |
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Authors: | Reinhard Winkler |
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Institution: | 1.?sterreichische Akademie der Wissenschaften, Wien, ?sterreich,AT |
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Abstract: | Let be a homomorphism with dense image in the compact group C. If is a continuity set, i.e. its topological boundary has Haar measure 0, then is called a Hartman set. If M is aperiodic then S contains the essential information about (C, ι) or, equivalently, about the dynamical system (C, T) where T is the ergodic group rotation . Using Pontryagin’s duality the paper presents a new method to get this information from S: The set S induces a filter on which is an isomorphism invariant for (C, T) and turns out to be a complete invariant for ergodic group rotations. If one takes , , , , one gets the interesting special case of Kronecker sequences (nα) which are classical objects in number theory and diophantine analysis.
Received 3 November 2000; in final form 25 January 2002 |
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Keywords: | : Monothetic groups group rotations group compactifications Hartman sets Hartman sequences Kronecker sequences |
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