Displaying similar documents to “Characterization of jacobian Newton polygons of plane branches and new criteria of irreducibility”

Note on the Newton number.

Gwoździewicz, Janusz (2008)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Indices of 1-forms and Newton polyhedra.

Alexander Esterov (2005)

Revista Matemática Complutense

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A formula of Matsuo Oka (1990) expresses the Milnor number of a germ of a complex analytic map with a generic principal part in terms of the Newton polyhedra of the components of the map. In this paper this formula is generalized to the case of the index of a 1-form on a local complete intersection singularity (Theorem 1.10, Corollaries 1.11, 4.1). In particular, the Newton polyhedron of a 1-form is defined (Definition 1.6). This also simplifies the Oka formula in some particular cases...

Immediate and Virtual Basins of Newton’s Method for Entire Functions

Sebastian Mayer, Dierk Schleicher (2006)

Annales de l’institut Fourier

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We investigate the well known Newton method to find roots of entire holomorphic functions. Our main result is that the immediate basin of attraction for every root is simply connected and unbounded. We also introduce “virtual immediate basins” in which the dynamics converges to infinity; we prove that these are simply connected as well.