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

A. Portela; J. Iglesias

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

J. Iglesias, A. Portela

Dynamical Systems · Submitted 21 Dec 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It is proved that the conditions are sufficient for $C^1$ stability in compact oriented manifolds of dimension two.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,595 input tokens.

What the abstract itself states, as probabilities: claims first 0.90 · states limitation 0.54 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.92 · mentions code or data availability 0.01.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

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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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A set of necessary conditions for $C^1$ stability of noninvertible maps is presented.	contribution 0.61	0.86	0.13	asserted 0.99
s1	It is proved that the conditions are sufficient for $C^1$ stability in compact oriented manifolds of dimension two.	result 0.95	0.90	0.71	asserted 1.00
s2	An example given by F.Przytycki in 1977 is shown to satisfy these conditions.	result 0.77	0.79	0.06	asserted 1.00
s3	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}	interpretation 0.43	0.54	0.29	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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arXiv listing abstract v1

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The paper

Original 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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