Stability modulo singular sets

Tom 204 / 2009

J. Iglesias, A. Portela, A. Rovella Fundamenta Mathematicae 204 (2009), 155-175 MSC: Primary 37C20; Secondary 58K05. DOI: 10.4064/fm204-2-5

Streszczenie

A new concept of stability, closely related to that of structural stability, is introduced and applied to the study of $C^1$ endomorphisms with singularities. A map that is stable in this sense is conjugate to each perturbation that is equivalent to it in a geometric sense. It is shown that this kind of stability implies Axiom A and ${\Omega }$-stability, and that every critical point is wandering. A partial converse is also shown, providing new examples of $C^3$ structurally stable maps.

Autorzy

  • J. IglesiasFacultad de Ingenieria, IMERL
    Universidad de La República
    Julio Herrera y Reissig 565
    Montevideo, Uruguay
    e-mail
  • A. PortelaFacultad de Ingenieria
    Universidad de La República, IMERL
    Julio Herrera y Reissig 565
    Montevideo, Uruguay
    e-mail
  • A. RovellaCentro de Matemática
    Facultad de Ciencias
    Universidad de La República
    Iguá 4225
    C.P. 11400, Montevideo, Uruguay
    e-mail

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