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## Fundamenta Mathematicae

2001 | 169 | 2 | 161-173
Tytuł artykułu

### Forcing relation on minimal interval patterns

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EN
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EN
Let ℳ be the set of pairs (T,g) such that T ⊂ ℝ is compact, g: T → T is continuous, g is minimal on T and has a piecewise monotone extension to convT. Two pairs (T,g),(S,f) from ℳ are equivalent if the map h: orb(minT,g) → orb(minS,f) defined for each m ∈ ℕ₀ by $h(g^m(minT)) = f^m(minS)$ is increasing on orb(minT,g). An equivalence class of this relation-a minimal (oriented) pattern A-is exhibited by a continuous interval map f:I → I if there is a set T ⊂ I such that (T,f|T) = (T,f) ∈ A. We define the forcing relation on minimal patterns: A forces B if all continuous interval maps exhibiting A also exhibit B. In Theorem 3.1 we show that for each minimal pattern A there are maps exhibiting only patterns forced by A. Using this result we prove that the forcing relation on minimal patterns is a partial ordering. Our Theorem 3.2 extends the result of [B], where pairs (T,g) with T finite are considered.
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Tom
Numer
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161-173
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Daty
wydano
2001
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autor
• KM FSv. ČVUT, Thákurova 7, 166 29 Praha 6, Czech Republic
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