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A fixed point theorem for branched covering maps of the plane

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Blokh A., Oversteegen L.

Fundamenta Mathematicae

2009

tom 206

nr 1

77-111

It is known that every homeomorphism of the plane which admits an invariant non-separating continuum has a fixed point in the continuum. In this paper we show that any branched covering map of the plane of degree d, |d| ≤ 2, which has an invariant, non-separating continuum Y, either has a fixed point in Y, or is such that Y contains a minimal (in the sense of inclusion among invariant continua), fully invariant, non-separating subcontinuum X. In the latter case, f has to be of degree -2 and X has exactly three fixed prime ends, one corresponding to an outchannel and the other two to inchannels.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Blokh A.

1 Oversteegen L.

1 2009

Wyniki wyszukiwania

A fixed point theorem for branched covering maps of the plane