$C^1$ stability of endomorphisms on two-dimensional manifolds

Volume 219 / 2012

J. Iglesias, A. Portela, A. Rovella Fundamenta Mathematicae 219 (2012), 37-58 MSC: Primary 37C75; Secondary 37C20. DOI: 10.4064/fm219-1-3

Abstract

A set of necessary conditions for $C^1$ stability of noninvertible maps is presented. It is proved that the conditions are sufficient for $C^1$ stability in compact oriented manifolds of dimension two. An example given by F. Przytycki in 1977 is shown to satisfy these conditions. It is the first example known of a $C^1$ stable map (noninvertible and nonexpanding) in a manifold of dimension two, while a wide class of examples are already known in every other dimension.

Authors

  • J. IglesiasIMERL
    Facultad de Ingeniería
    Universidad de La República
    Julio Herrera y Reissig 565
    C.P. 11300, Montevideo, Uruguay
    e-mail
  • A. PortelaIMERL
    Facultad de Ingeniería
    Universidad de La República
    Julio Herrera y Reissig 565
    C.P. 11300, Montevideo, Uruguay
    e-mail
  • A. RovellaIMERL
    Facultad de Ingeniería
    Universidad de La República
    Julio Herrera y Reissig 565
    C.P. 11300, Montevideo, Uruguay
    e-mail

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