C¹ stability of endomorphisms on two-dimensional manifolds

J. Iglesias, A. Portela, and A. Rovella. "C¹ stability of endomorphisms on two-dimensional manifolds." Fundamenta Mathematicae 219.1 (2012): 37-58. <http://eudml.org/doc/286093>.

@article{J2012,
abstract = {A set of necessary conditions for C¹ stability of noninvertible maps is presented. It is proved that the conditions are sufficient for C¹ 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 C¹ stable map (noninvertible and nonexpanding) in a manifold of dimension two, while a wide class of examples are already known in every other dimension.},
author = {J. Iglesias, A. Portela, A. Rovella},
journal = {Fundamenta Mathematicae},
keywords = {structural stability; stability; endomorphism in dimension two},
language = {eng},
number = {1},
pages = {37-58},
title = {C¹ stability of endomorphisms on two-dimensional manifolds},
url = {http://eudml.org/doc/286093},
volume = {219},
year = {2012},
}

TY - JOUR
AU - J. Iglesias
AU - A. Portela
AU - A. Rovella
TI - C¹ stability of endomorphisms on two-dimensional manifolds
JO - Fundamenta Mathematicae
PY - 2012
VL - 219
IS - 1
SP - 37
EP - 58
AB - A set of necessary conditions for C¹ stability of noninvertible maps is presented. It is proved that the conditions are sufficient for C¹ 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 C¹ stable map (noninvertible and nonexpanding) in a manifold of dimension two, while a wide class of examples are already known in every other dimension.
LA - eng
KW - structural stability; stability; endomorphism in dimension two
UR - http://eudml.org/doc/286093
ER -