Periodicity generated by adding machines

Authors

  • K. Kuperberg Department of Mathematics, Auburn University

Abstract

We show that a homeomorphism of the plane R2 with an invariant Cantor set C, on which the homeomorphism acts as an adding machine, possesses periodic points arbitrarily close to C. The existence of periodic points near an invariant Cantor set is related to a shape theory question whether a solenoid invariant in a flow defined on R3 must be contained in a larger movable invariant compactum.

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Published

2013-06-26

How to Cite

Kuperberg, K. (2013). Periodicity generated by adding machines. Transactions of Institute of Mathematics, the NAS of Ukraine, 10(6), 140–147. Retrieved from https://trim.imath.kiev.ua/index.php/trim/article/view/310