Geodesic
$C^1$ stability of endomorphisms on two-dimensional manifolds
J. Iglesias 1   ; A. Portela 1   ; A. Rovella 1
1 IMERL Facultad de Ingeniería Universidad de La República Julio Herrera y Reissig 565 C.P. 11300, Montevideo, Uruguay
Fundamenta Mathematicae, Tome 219 (2012) no. 1, pp. 37-58 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm219-1-3
Keywords: set necessary conditions stability noninvertible maps presented proved conditions sufficient stability compact oriented manifolds dimension example given nbsp przytycki shown satisfy these conditions first example known stable map noninvertible nonexpanding manifold dimension while wide class examples already known every other dimension

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

1 IMERL Facultad de Ingeniería Universidad de La República Julio Herrera y Reissig 565 C.P. 11300, Montevideo, Uruguay 
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J. Iglesias; A. Portela; A. Rovella. $C^1$ stability of endomorphisms on two-dimensional manifolds. Fundamenta Mathematicae, Tome 219 (2012) no. 1, pp. 37-58. doi: 10.4064/fm219-1-3

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