Displaying similar documents to “On the topological triviality along moduli of deformations of J k , 0 singularities”

On blowing up versal discriminants

Piotr Jaworski (1998)

Banach Center Publications

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It is well-known that the versal deformations of nonsimple singularities depend on moduli. The first step in deeper understanding of this phenomenon is to determine the versal discriminant, which roughly speaking is an obstacle for analytic triviality of an unfolding or deformation along the moduli. The goal of this paper is to describe the versal discriminant of Z k , 0 and Q k , 0 singularities basing on the fact that the deformations of these singularities may be obtained as blowing ups of certain...

On the versal discriminant of J k , 0 singularities

Piotr Jaworski (1996)

Annales Polonici Mathematici

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It is well known that the versal deformations of nonsimple singularities depend on moduli. The first step in deeper understanding of this phenomenon is to determine the versal discriminant, which roughly speaking is an obstacle to analytic triviality of an unfolding or deformation along the moduli. The versal discriminant of the Pham singularity ( J 3 , 0 in Arnold’s classification) was thoroughly investigated by J. Damon and A. Galligo [2], [3], [4]. The goal of this paper is to continue their...

Decompositions of hypersurface singularities oftype J k , 0

Piotr Jaworski (1994)

Annales Polonici Mathematici

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Applications of singularity theory give rise to many questions concerning deformations of singularities. Unfortunately, satisfactory answers are known only for simple singularities and partially for unimodal ones. The aim of this paper is to give some insight into decompositions of multi-modal singularities with unimodal leading part. We investigate the J k , 0 singularities which have modality k - 1 but the quasihomogeneous part of their normal form only depends on one modulus.

Some division theorems for vector fields

Andrzej Zajtz (1993)

Annales Polonici Mathematici

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This paper is concerned with the problem of divisibility of vector fields with respect to the Lie bracket [X,Y]. We deal with the local divisibility. The methods used are based on various estimates, in particular those concerning prolongations of dynamical systems. A generalization to polynomials of the adjoint operator (X) is given.

Simultaneous reduction to normal forms of commuting singular vector fields with linear parts having Jordan blocks

Masafumi Yoshino, Todor Gramchev (2008)

Annales de l’institut Fourier

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We study the simultaneous linearizability of d –actions (and the corresponding d -dimensional Lie algebras) defined by commuting singular vector fields in ℂ n fixing the origin with nontrivial Jordan blocks in the linear parts. We prove the analytic convergence of the formal linearizing transformations under a certain invariant geometric condition for the spectrum of d vector fields generating a Lie algebra. If the condition fails and if we consider the situation where small denominators...

On the Łojasiewicz exponent for analytic curves

Jacek Chądzyński, Tadeusz Krasiński (1998)

Banach Center Publications

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An effective formula for the Łojasiewicz exponent for analytic curves in a neighbourhood of 0 ∈ ℂ is given.