A classification of inverse limit spaces of tent maps with periodic critical points

• Autorzy: Lois Kailhofer
• Języki publikacji: EN

Abstrakty

EN

We work within the one-parameter family of symmetric tent maps, where the slope is the parameter. Given two such tent maps $f_a$, $f_b$ with periodic critical points, we show that the inverse limit spaces $(𝕀_a,f_a)$ and $(𝕀_b,g_b)$ are not homeomorphic when a ≠ b. To obtain our result, we define topological substructures of a composant, called "wrapping points" and "gaps", and identify properties of these substructures preserved under a homeomorphism.

Kategorie tematyczne

• 54H20: Topological dynamics
• 54F15: Continua and generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 177
• Numer: 2
• Strony: 95-120

Daty

wydano

2003

Twórcy

autor

Lois Kailhofer

• Department of Mathematics, Alverno College, 3401 S 39th, Milwaukee, WI 53215, U.S.A.

Identyfikatory

DOI

10.4064/fm177-2-1