We construct homeomorphisms of R2 that have a Cantor set which is a minimal set. Some of these homeomorphisms are proven to be C^(infinity), while the others are conjectured to be nondifferentiable (Refer to PDF file for exact formulas).
Department, Program, or Center
School of Mathematical Sciences (COS)
William Basener and Carl V. Lutzer, Twisted Solenoids and Maps of R2 Whose Minimal Sets Are Cantor Sets, Top. Proc. 30, no 1 (2006) pp. 69-81.
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