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Moduli of stability for germs of homogeneous vectorfields on $$R^ 3$$. (English) Zbl 0633.58031
It is well known that a finite classification for the homogeneous quadratic vector fields in the plane is possible. The authors construct an example of an uncountable family of homogeneous quadratic vector fields $$X_ a$$ in $$R^ 3$$. They prove two theorems. Theorem A: If $$X_ a$$ is topologically equivalent to $$X_{a'}$$, at the origin in $$R^ 3$$ then $$a=a'$$. Theorem $$B: X_ a$$ have a nonstabilizable modulus of stability on the 2-jet level in the following sense. If $$Y_ a$$ and $$Y_{a'}$$ are vector fields such that $$X_ a$$, $$Y_ a$$ and $$Y_{a'}$$ have the same Taylor expansion at the origin up to order 2, then $$a\neq a'$$ implies that $$Y_ a$$ and $$Y_{a'}$$ are topologically nonequivalent at the origin. The bibliography contains 37 items.
Reviewer: A.Kanevskij

##### MSC:
 37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
##### Keywords:
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