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

J. Delgado; N. Romero; A. Rovella; F. Vilamajó

doi:10.4064/fm193-1-3

Geodesic

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

J. Delgado ¹ ; N. Romero ² ; A. Rovella ³ ; F. Vilamajó ⁴

¹ Instituto de Matemática Universidade Federal Fluminense Rua Mario Santos Braga S.N. CEP 24020-140 Niterói (RJ), Brasil
² Departamento de Matemáticas, apdo. 400 Decanato de Ciencias y Tecnología Universidad Centroccidental Lisandro Alvarado Barquisimeto, Venezuela
³ Centro de Matematica Facultad de Ciencias Universidad de La República Iguá 4225, C.P. 11400 Montevideo, Uruguay
⁴ Departament de Matemàtica Aplicada 2 Escola Tècnica Superior D'Enginyeria Industrial Universidad Politècnica de Catalunya Colom 11, 08222 Terrasa, Barcelona, Spain

Fundamenta Mathematicae, Tome 193 (2007) no. 1, pp. 23-35.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Résumé

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.

DOI : 10.4064/fm193-1-3

Keywords: sufficient conditions map having nonwandering critical points mit omega stable introduced known these conditions necessary easily verified known examples mit omega stable maps their necessity shown dimension examples given axiom maps have cycles mit omega stable

Affiliations des auteurs :

J. Delgado ¹ ; N. Romero ² ; A. Rovella ³ ; F. Vilamajó ⁴

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J. Delgado; N. Romero; A. Rovella; F. Vilamajó. $\Omega $-stability for maps with nonwandering critical points. Fundamenta Mathematicae, Tome 193 (2007) no. 1, pp. 23-35. doi : 10.4064/fm193-1-3. http://geodesic.mathdoc.fr/articles/10.4064/fm193-1-3/

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