Eventual colorings of homeomorphisms

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 ev...

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Bibliographic Details
Published in:Journal of the Mathematical Society of Japan 2013, Vol.65 (2), p.375-387
Main Authors: IKEGAMI, Yuki, KATO, Hisao, UEDA, Akihide
Format: Article
Language:English
Subjects:
54C05
54F45
54H20
55M10
55M30
coloring
dimension
eventual coloring
fixed-point free homeomorphism
periodic point
topological dynamics
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Summary: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.
ISSN:0025-5645
1881-2333
DOI:10.2969/jmsj/06520375