Displaying similar documents to “Supplement to the paper 'Quasianalytic perturbation of multi-parameter hyperbolic polynomials and symmetric matrices' (Ann. Polon. Math. 101 (2011), 275-291)”

Quasianalytic perturbation of multi-parameter hyperbolic polynomials and symmetric matrices

Krzysztof Jan Nowak (2011)

Annales Polonici Mathematici

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This paper investigates hyperbolic polynomials with quasianalytic coefficients. Our main purpose is to prove factorization theorems for such polynomials, and next to generalize the results of K. Kurdyka and L. Paunescu about perturbation of analytic families of symmetric matrices to the quasianalytic setting.

Convergence of pinching deformations and matings of geometrically finite polynomials

Peter Haïssinsky, Lei Tan (2004)

Fundamenta Mathematicae

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We give a thorough study of Cui's control of distortion technique in the analysis of convergence of simple pinching deformations, and extend his result from geometrically finite rational maps to some subset of geometrically infinite maps. We then combine this with mating techniques for pairs of polynomials to establish existence and continuity results for matings of polynomials with parabolic points. Consequently, if two hyperbolic quadratic polynomials tend to their respective root...

Even and Old Overdetermined Strata for Degree 6 Hyperbolic Polynomials

Ezzaldine, Hayssam, Kostov, Vladimir Petrov (2008)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 12D10. In the present paper we consider degree 6 hyperbolic polynomials (HPs) in one variable (i.e. real and with all roots real). We are interested in such HPs whose number of equalities between roots of the polynomial and/or its derivatives is higher than expected. We give the complete study of the four families of such degree 6 even HPs and also of HPs which are primitives of degree 5 HPs. Research partially supported...

Integer Linear Programming applied to determining monic hyperbolic irreducible polynomials with integer coefficients and span less than 4

Souad El Otmani, Armand Maul, Georges Rhin, Jean-Marc Sac-Épée (2013)

Journal de Théorie des Nombres de Bordeaux

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In this work, we propose a new method to find monic irreducible polynomials with integer coefficients, only real roots, and span less than 4. The main idea is to reduce the search of such polynomials to the solution of Integer Linear Programming problems. In this frame, the coefficients of the polynomials we are looking for are the integer unknowns. We give inequality constraints specified by the properties that the polynomials should have, such as the typical distribution of their roots....