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2005 On trajectories of analytic gradient vector fields on analytic manifolds
Aleksandra Nowel, Zbigniew Szafraniec
Topol. Methods Nonlinear Anal. 25(1): 167-182 (2005).

Abstract

Let $f\colon M\to {\mathbb R}$ be an analytic proper function defined in a neighbourhood of a closed "regular" (for instance semi-analytic or sub-analytic) set $P\subset f^{-1}(y)$. We show that the set of non-trivial trajectories of the equation $\dot x =\nabla f(x)$ attracted by $P$ has the same Čech-Alexander cohomology groups as $\Omega\cap\{f< y\}$, where $\Omega$ is an appropriately choosen neighbourhood of $P$. There are also given necessary conditions for existence of a trajectory joining two closed "regular" subsets of $M$.

Citation

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Aleksandra Nowel. Zbigniew Szafraniec. "On trajectories of analytic gradient vector fields on analytic manifolds." Topol. Methods Nonlinear Anal. 25 (1) 167 - 182, 2005.

Information

Published: 2005
First available in Project Euclid: 23 June 2016

zbMATH: 1084.37016
MathSciNet: MR2133397

Rights: Copyright © 2005 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.25 • No. 1 • 2005
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