Wandering sets for a class of borel isomorphisms of [0,1) |
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Authors: | Edward A. Azoff Eugen J. Ionascu |
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Affiliation: | (1) The University of Georgia, 30602 Athens, GA;(2) Columbus State University, 31907 Columbus, GA |
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Abstract: | A wandering set for a map ϕ is a set containing precisely one element from each orbit of ϕ. We study the existence of Borel wandering sets for piecewise linear isomorphisms. Such sets need not exist even when the parameters involved are rational, but they do exist if in addition all the slopes are powers of 2. For ϕ having at most one discontinuity, the existence of a Borel wandering set is equivalent to rationality of the Poincaré rotation number. We compute the rotation numbers for a special class of such functions. The main result provides a concrete method of connecting certain pairs of wavelet sets. |
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Keywords: | primary 37E05, 28B20, 54C65 secondary 26A18, 37A05, 37E10, 42C15 |
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