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

100%

Kailhofer L.

Fundamenta Mathematicae

2003

tom 177

nr 2

95-120

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.

On the classification of inverse limits of tent maps

51%

Block L., Jakimovik S., Kailhofer L., Keesling J.

Fundamenta Mathematicae

2005

tom 187

nr 2

171-192

Let $f_s$ and $f_t$ be tent maps on the unit interval. In this paper we give a new proof of the fact that if the critical points of $f_s$ and $f_t$ are periodic and the inverse limit spaces $(I,f_s)$ and $(I,f_t)$ are homeomorphic, then s = t. This theorem was first proved by Kailhofer. The new proof in this paper simplifies the proof of Kailhofer. Using the techniques of the paper we are also able to identify certain isotopies between homeomorphisms on the inverse limit space.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Kailhofer L.

1 Block L.

1 Jakimovik S.

1 Keesling J.

1 2005

1 2003

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

On the classification of inverse limits of tent maps