We introduce a blowing-up of singularities of vector fields associated with Newton Polyhedra in the space of the exponents, by means of which we prove a generalization of the Hartman-Grobman Theorem, namely: a plane vector field possessing characteristic orbits is locally topologically equivalent with its principal part, under suitable non-degeneracy hypotheses. Under stronger hypotheses, a similar equivalence result is proven between a plane vector field and a single quasihomogeneous component of its principal part. The case of second order equations is also studied.
Topological equivalence of a plane vector field with its principal part defined through Newton Polyhedra
MIARI, MASSIMO
1990-01-01
Abstract
We introduce a blowing-up of singularities of vector fields associated with Newton Polyhedra in the space of the exponents, by means of which we prove a generalization of the Hartman-Grobman Theorem, namely: a plane vector field possessing characteristic orbits is locally topologically equivalent with its principal part, under suitable non-degeneracy hypotheses. Under stronger hypotheses, a similar equivalence result is proven between a plane vector field and a single quasihomogeneous component of its principal part. The case of second order equations is also studied.File in questo prodotto:
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