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Adding machines as invariant sets for homeomorphisms of a disk into the plane

Published online by Cambridge University Press:  10 April 2006

MARCIN KULCZYCKI
MARCIN KULCZYCKI
Affiliation:
Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland (e-mail: marcin.kulczycki@im.uj.edu.pl)
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Abstract

Let $h:D\rightarrow {\mathbb R}^2$ be a homeomorphism of a disk into the plane. Let $C\subset {\rm int}\,D$ be a Cantor set such that $(C,h|_C)$ is an adding machine. We give a condition under which there are points outside of C which have their entire orbits contained in D.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 3 , June 2006 , pp. 783 - 786
Copyright
2006 Cambridge University Press

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