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Conjugacy of normally tangent diffeomorphisms : a tool for treating moduli of stability

Patrick Bonckaert — 1990

Annales de l'institut Fourier

We give sufficient conditions for the conjugacy of two diffeomorphisms coinciding on a common invariant submanifold V and with equal normal derivative; moreover we obtain that the homeomorphism h realizing this conjugacy satisfies additional inequalities. These inequalities, implying also the existence of the normal derivative of h along V, serve to extend this conjugacy towards regions where moduli of stability are present.

Smooth invariant curves of singularities of vector fields on $ℝ^{3}$

Patrick Bonckaert — 1986

Annales de l'I.H.P. Analyse non linéaire

On a Linearization Theorem of Sternberg for Germs of Diffeomorphisms.

Patrick Bonckaert; Freddy Dumortier — 1984

Mathematische Zeitschrift

Normal forms with exponentially small remainder and Gevrey normalization for vector fields with a nilpotent linear part

Patrick Bonckaert; Freek Verstringe — 2012

Annales de l’institut Fourier

We explore the convergence/divergence of the normal form for a singularity of a vector field on $ℂ^{n}$ with nilpotent linear part. We show that a Gevrey- $α$ vector field $X$ with a nilpotent linear part can be reduced to a normal form of Gevrey- $1 + α$ type with the use of a Gevrey- $1 + α$ transformation. We also give a proof of the existence of an optimal order to stop the normal form procedure. If one stops the normal form procedure at this order, the remainder becomes exponentially small.

Asymptotic properties of the Dulac map near a hyperbolic saddle in dimension three

Patrick Bonckaert; Vincent Naudot — 2001

Annales de la Faculté des sciences de Toulouse : Mathématiques

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Currently displaying 1 – 5 of 5

Conjugacy of normally tangent diffeomorphisms : a tool for treating moduli of stability

Smooth invariant curves of singularities of vector fields on $ℝ^{3}$

On a Linearization Theorem of Sternberg for Germs of Diffeomorphisms.

Normal forms with exponentially small remainder and Gevrey normalization for vector fields with a nilpotent linear part

Asymptotic properties of the Dulac map near a hyperbolic saddle in dimension three

Advanced Search

Formula preview

Currently displaying 1 – 5 of 5

Conjugacy of normally tangent diffeomorphisms : a tool for treating moduli of stability

Smooth invariant curves of singularities of vector fields on ℝ 3

On a Linearization Theorem of Sternberg for Germs of Diffeomorphisms.

Normal forms with exponentially small remainder and Gevrey normalization for vector fields with a nilpotent linear part

Asymptotic properties of the Dulac map near a hyperbolic saddle in dimension three

Smooth invariant curves of singularities of vector fields on $ℝ^{3}$