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newton non-degeneracy conditions

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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On the number of topological orbits of complex germs in classes (xy, xa + yb )
Part of
- Singularities
- Theory of singularities and catastrophe theory
Aldicio José Miranda, Liane Mendes Feitosa Soares, Marcelo José Saia
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 147 / Issue 1 / February 2017

Published online by Cambridge University Press:

27 October 2016, pp. 205-224

Print publication:

February 2017
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We show that there exist an infinite number of topological orbits in classes of complex map germs from the plane to the plane that have a representative of type (xy, xa + yb ), with (a, b) ≠ = (2, 3) or (2, 5). Our key tool to prove this existence is the existence (or not) of stems in the class; these germs are not -finitely determined and allow the determination of a non-finite number of topological orbits. We also show that the class (xy, x 2 + y 5) has two topological orbits.