Forcing relation on minimal interval patterns

• Autorzy: Jozef Bobok
• Języki publikacji: EN

Abstrakty

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.

Kategorie tematyczne

• 37E99: None of the above, but in this section
• 26A18: Iteration
• 37E05: Maps of the interval (piecewise continuous, continuous, smooth)
• 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2001
• Tom: 169
• Numer: 2
• Strony: 161-173

Daty

wydano

2001

Twórcy

autor

Jozef Bobok

• KM FSv. ČVUT, Thákurova 7, 166 29 Praha 6, Czech Republic

Identyfikatory

DOI

10.4064/fm169-2-5