Exceptional sets and Antoine's necklace

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Title: Exceptional sets and Antoine's necklace
Author: Basener, William
Abstract: We study Cantor sets which occur as minimal sets for homeomorphisms of R^n. The minimality is modelled on an infinite product of finite cyclic groups and on a generalized adding machine. An interesting example is a homeomorphisms on R^3 which has Antoine’s Necklace as a minimal set. We also discuss some open problems concerning homeomorphism that have a Cantor set as a minimal set (Refer to PDF file for exact formulas).
Record URI: http://hdl.handle.net/1850/4743
Date: 2007-09-13

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