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Didier D'Acunto, Vincent Grandjean (2005)
Revista Matemática Complutense
Let f be a C1 function defined over Rn and definable in a given o-minimal structure M expanding the real field. We prove here a gradient-like inequality at infinity in a neighborhood of an asymptotic critical value c. When f is C2 we use this inequality to discuss the trivialization by the gradient flow of f in a neighborhood of a regular asymptotic critical level.
M. Sabatini (2009)
Bulletin of the Polish Academy of Sciences. Mathematics
We give a shorter proof to a recent result by Neuberger [Rocky Mountain J. Math. 36 (2006)], in the real case. Our result is essentially an application of the global asymptotic stability Jacobian Conjecture. We also extend some of the results of Neuberger's paper.
Hossein Movasati (2004)
Revista Matemática Iberoamericana
The aim of this paper is to introduce the theory of Abelian integrals for holomorphic foliations in a complex manifold of dimension two. We will show the importance of Picard-Lefschetz theory and the classification of relatively exact 1-forms in this theory. As an application we identify some irreducible components of the space of holomorphic foliations of a fixed degree and with a center singularity in the projective space of dimension two. Also we calculate higher Melnikov functions under some...
Khukhunashvili, Z.V., Khukhunashvili, Z.Z. (2001)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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