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Summer 1999 Injectivity as a transversality phenomenon in geometries of negative curvature
Frederico Xavier
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Illinois J. Math. 43(2): 256-263 (Summer 1999). DOI: 10.1215/ijm/1255985213


The global asymptotic stability conjecture in dynamical systems was solved recently and independently by Feller, Glutsiuk and Gutierrez. Crucial to the approach of Gutierrez is the following theorem of his: A local diffeomorphism $f:\mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ for which the eigenvalues of $Df(x)$ miss $(0,\infty)$ must be injective. The present paper gives a partial generalization of this theorem to local diffeomorphisms between Hadamard surfaces, the spectral condition being replaced by transversality conditions among certain foliations associated to horocycles. The proofs use arguments from global analysis.


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Frederico Xavier. "Injectivity as a transversality phenomenon in geometries of negative curvature." Illinois J. Math. 43 (2) 256 - 263, Summer 1999.


Published: Summer 1999
First available in Project Euclid: 19 October 2009

zbMATH: 0965.58013
MathSciNet: MR1703186
Digital Object Identifier: 10.1215/ijm/1255985213

Primary: 53C21

Rights: Copyright © 1999 University of Illinois at Urbana-Champaign

Vol.43 • No. 2 • Summer 1999
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