Open Access
April, 2013 Eventual colorings of homeomorphisms
Yuki IKEGAMI, Hisao KATO, Akihide UEDA
J. Math. Soc. Japan 65(2): 375-387 (April, 2013). DOI: 10.2969/jmsj/06520375


In this paper, we study some dynamical properties of fixed-point free homeomorphisms of separable metric spaces. For each natural number $p$, we define eventual colorings within $p$ of homeomorphisms which are generalized notions of colorings of fixed-point free homeomorphisms, and we investigate the eventual coloring number $C(f,p)$ of a fixed-point free homeomorphism $f: X \to X$ with zero-dimensional set of periodic points. In particular, we show that if $\dim X$ < $\infty$, then there is a natural number $p$, which depends on $\dim X$, and $X$ can be divided into two closed regions $C_{1}$ and $C_{2}$ such that for each point $x\in X$, the orbit $\{f^{k}(x)\}_{k=0}^{\infty}$ of $x$ goes back and forth between $C_1-C_2$ and $C_2-C_1$ within the time $p$.


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Yuki IKEGAMI. Hisao KATO. Akihide UEDA. "Eventual colorings of homeomorphisms." J. Math. Soc. Japan 65 (2) 375 - 387, April, 2013.


Published: April, 2013
First available in Project Euclid: 25 April 2013

zbMATH: 1275.54020
MathSciNet: MR3055590
Digital Object Identifier: 10.2969/jmsj/06520375

Primary: 54F45 , 54H20‎
Secondary: 54C05 , 55M10 , 55M30

Keywords: coloring , dimension , eventual coloring , fixed-point free homeomorphism , periodic point , topological dynamics

Rights: Copyright © 2013 Mathematical Society of Japan

Vol.65 • No. 2 • April, 2013
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