Periodicity generated by adding machines

• Datum: 2013
• 1. Verfasser: Kuperberg, K.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2013
• Online Zugang: https://trim.imath.kiev.ua/index.php/trim/article/view/310
• Назва журналу: Transactions of Institute of Mathematics of NAS of Ukraine

We show that a homeomorphism of the plane $\mathbb{R}^2$ with an invariant Cantor set $\mathbf {C}$, on which the homeomorphism acts as an adding machine, possesses periodic points arbitrarily close to $\mathbf {C}$. The existence of periodic points near an invariant Cantor set is related to a shape...