A fixed point theorem for branched covering maps of the plane

• Autorzy: Alexander Blokh , Lex Oversteegen
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37C25: Fixed points, periodic points, fixed-point index theory
• 37B45: Continua theory in dynamics
• 54H25: Fixed-point and coincidence theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 206
• Numer: 1
• Strony: 77-111

Daty

wydano

2009

Twórcy

autor

Alexander Blokh

• Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294-1170, U.S.A.

autor

Lex Oversteegen

• Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294-1170, U.S.A.

Identyfikatory

DOI

10.4064/fm206-0-6