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The construction of P-expansive maps of regular continua: A geometric approach

✍ Scribed by Tatsuya Arai; Naotsugu Chinen; Hisao Kato; Katsuya Yokoi

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 223 KB
Volume: 103
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(99)00004-8

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✦ Synopsis

In this paper, we prove the following: Let G be a graph, f : G → G a continuous map and P a finite subset of G such that f (P ) ⊂ P . Then there exist a regular continuum Z, a continuous map g : Z → Z and a semi-conjugacy π : G → Z such that

(1) g is π(P )-expansive, and

(2) if p, q ∈ P and Q is a subset of P with A ∩ Q = ∅ for any arc A in G between p and q, then A ∩ π(Q) = ∅ for any arc A in Z between π(p) and π(q).

In addition, f is point-wise P -expansive if and only if π| P is one-to-one.

In this paper we are especially interested in the geometrical structure of Z. Actually we can see the complicated construction of Z.

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