Displaying similar documents to “A theorem on the escape from the space of hyperbolic polynomials.”

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.

Supplement to the paper "Quasianalytic perturbation of multi-parameter hyperbolic polynomials and symmetric matrices" (Ann. Polon. Math. 101 (2011), 275-291)

Krzysztof Jan Nowak (2012)

Annales Polonici Mathematici

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In IMUJ Preprint 2009/05 we investigated the quasianalytic perturbation of hyperbolic polynomials and symmetric matrices by applying our quasianalytic version of the Abhyankar-Jung theorem from IMUJ Preprint 2009/02, whose proof relied on a theorem by Luengo on ν-quasiordinary polynomials. But those papers of ours were suspended after we had become aware that Luengo's paper contained an essential gap. This gave rise to our subsequent article on quasianalytic perturbation theory, which...

Boundaries of right-angled hyperbolic buildings

Jan Dymara, Damian Osajda (2007)

Fundamenta Mathematicae

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We prove that the boundary of a right-angled hyperbolic building is a universal Menger space. As a consequence, the 3-dimensional universal Menger space is the boundary of some Gromov-hyperbolic group.