Geodesic
Stability modulo singular sets
J. Iglesias 1   ; A. Portela 2   ; A. Rovella 3
1 Facultad de Ingenieria, IMERL Universidad de La República Julio Herrera y Reissig 565 Montevideo, Uruguay
2 Facultad de Ingenieria Universidad de La República, IMERL Julio Herrera y Reissig 565 Montevideo, Uruguay
3 Centro de Matemática Facultad de Ciencias Universidad de La República Iguá 4225 C.P. 11400, Montevideo, Uruguay
Fundamenta Mathematicae, Tome 204 (2009) no. 2, pp. 155-175 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm204-2-5
Keywords: concept stability closely related structural stability introduced applied study endomorphisms singularities map stable sense conjugate each perturbation equivalent geometric sense shown kind stability implies axiom omega stability every critical point wandering partial converse shown providing examples structurally stable maps

J. Iglesias  1   ; A. Portela  2   ; A. Rovella  3

1 Facultad de Ingenieria, IMERL Universidad de La República Julio Herrera y Reissig 565 Montevideo, Uruguay
2 Facultad de Ingenieria Universidad de La República, IMERL Julio Herrera y Reissig 565 Montevideo, Uruguay
3 Centro de Matemática Facultad de Ciencias Universidad de La República Iguá 4225 C.P. 11400, Montevideo, Uruguay 
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J. Iglesias; A. Portela; A. Rovella. Stability modulo singular sets. Fundamenta Mathematicae, Tome 204 (2009) no. 2, pp. 155-175. doi: 10.4064/fm204-2-5

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