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arXiv · 1712.08114

$C^1$ stability of endomorphisms on two dimensional manifolds

J. Iglesias·A. Portela
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Abstract

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. \end{abstract}

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J. Iglesias, A. Portela. 2017-12-21. $C^1$ stability of endomorphisms on two dimensional manifolds. https://arxiv.org/abs/1712.08114

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