$\Omega $-stability for maps with nonwandering critical points

Volume 193 / 2007

J. Delgado, N. Romero, A. Rovella, F. Vilamajó Fundamenta Mathematicae 193 (2007), 23-35 MSC: Primary 37D20. DOI: 10.4064/fm193-1-3


Sufficient conditions for a map having nonwandering critical points to be ${\mit\Omega} $-stable are introduced. It is not known if these conditions are necessary, but they are easily verified for all known examples of ${\mit\Omega} $-stable maps. Their necessity is shown in dimension two. Examples are given of Axiom~A maps that have no cycles but are not ${\mit\Omega} $-stable.


  • J. DelgadoInstituto de Matemática
    Universidade Federal Fluminense
    Rua Mario Santos Braga S.N.
    CEP 24020-140 Niterói (RJ), Brasil
  • N. RomeroDepartamento de Matemáticas, apdo. 400
    Decanato de Ciencias y Tecnología
    Universidad Centroccidental Lisandro Alvarado
    Barquisimeto, Venezuela
  • A. RovellaCentro de Matematica
    Facultad de Ciencias
    Universidad de La República
    Iguá 4225, C.P. 11400
    Montevideo, Uruguay
  • F. VilamajóDepartament de Matemàtica Aplicada 2
    Escola Tècnica Superior D'Enginyeria Industrial
    Universidad Politècnica de Catalunya
    Colom 11, 08222 Terrasa, Barcelona, Spain

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