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Homeomorphisms of composants of Knaster continua

100%

Štimac S.

Fundamenta Mathematicae

2002

tom 171

nr 3

267-278

The Knaster continuum $K_p$ is defined as the inverse limit of the pth degree tent map. On every composant of the Knaster continuum we introduce an order and we consider some special points of the composant. These are used to describe the structure of the composants. We then prove that, for any integer p ≥ 2, all composants of $K_p$ having no endpoints are homeomorphic. This generalizes Bandt's result which concerns the case p = 2.

Structure of inverse limit spaces of tent maps with finite critical orbit

100%

Štimac S.

Fundamenta Mathematicae

2006

tom 191

nr 2

125-150

Using methods of symbolic dynamics, we analyze the structure of composants of the inverse limit spaces of tent maps with finite critical orbit. We define certain symmetric arcs called bridges. They are building blocks of composants. Then we show that the folding patterns of bridges are characterized by bridge types and prove that there are finitely many bridge types.

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2 Fundamenta Mathematicae

2 Štimac S.

1 2006

1 2002

Wyniki wyszukiwania

Homeomorphisms of composants of Knaster continua

Structure of inverse limit spaces of tent maps with finite critical orbit