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A gradient inequality at infinity for tame functions.

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.

A note on the fundamental matrix of variational equations in 3

Ladislav Adamec (2003)

Mathematica Bohemica

The paper is devoted to the question whether some kind of additional information makes it possible to determine the fundamental matrix of variational equations in 3 . An application concerning computation of a derivative of a scalar Poincaré mapping is given.

Commutators of flows and fields

Markus Mauhart, Peter W. Michor (1992)

Archivum Mathematicum

The well known formula [ X , Y ] = 1 2 2 t 2 | 0 ( - t Y ø - t X ø t Y ø t X ) for vector fields X , Y is generalized to arbitrary bracket expressions and arbitrary curves of local diffeomorphisms.

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