PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Fixed points for branched covering maps of the plane

Volume 254 / 2021

Alejo García Sassi Fundamenta Mathematicae 254 (2021), 1-14 MSC: Primary 37B20; Secondary 37E30. DOI: 10.4064/fm765-4-2020 Published online: 10 December 2020


A well-known result of Brouwer states that any orientation preserving homeomorphism of the plane with no fixed points has an empty non-wandering set. In particular, the existence of an invariant compact set implies the existence of a fixed point. In this paper we give sufficient conditions for degree 2 branched covering maps of the plane to have a fixed point, namely:
$\bullet$ A totally invariant compact subset that does not separate the critical point from its image.
$\bullet$ An invariant compact subset with a connected neighbourhood $B$ such that $\mathrm {Fill}(B \cup f(B))$ does not contain the critical point nor its image.
$\bullet$ An invariant continuum such that the critical point and its image belong to the same connected component of its complement.


  • Alejo García SassiInstituto de Matemática y Estadística
    Facultad de Ingeniería
    Universidad de la República
    Julio Herrera y Reissig 565
    11300 Montevideo, Uruguay

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image