Normal forms for certain singularities of vectorfields

Floris Takens

Displaying similar documents to “Normal forms for certain singularities of vectorfields”

Holonomy groups of complete flat manifolds

Michał Sadowski (2007)

Banach Center Publications

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We present short direct proofs of two known properties of complete flat manifolds. They say that the diffeomorphism classes of m-dimensional complete flat manifolds form a finite set $S_{C F} (m)$ and that each element of $S_{C F} (m)$ is represented by a manifold with finite holonomy group.

A generalization of Thom’s transversality theorem

Lukáš Vokřínek (2008)

Archivum Mathematicum

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We prove a generalization of Thom’s transversality theorem. It gives conditions under which the jet map $f_{*} |_{Y} : Y \subseteq J^{r} (D, M) \to J^{r} (D, N)$ is generically (for $f : M \to N$ ) transverse to a submanifold $Z \subseteq J^{r} (D, N)$ . We apply this to study transversality properties of a restriction of a fixed map $g : M \to P$ to the preimage ${(j^{s} f)}^{- 1} (A)$ of a submanifold $A \subseteq J^{s} (M, N)$ in terms of transversality properties of the original map $f$ . Our main result is that for a reasonable class of submanifolds $A$ and a generic map $f$ the restriction ${g |}_{{(j^{s} f)}^{- 1} (A)}$ is also generic. We also present an example...

Simple singularities of multigerms of curves.

Pavel A. Kolgushkin, Ruslan R. Sadykov (2001)

Revista Matemática Complutense

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We classify stably simple reducible curve singularities in complex spaces of any dimension. This extends the same classification of irreducible curve singuarities obtained by V. I. Arnold. The proof is essentially based on the method of complete transversals by J. Bruce et al.

On the classification of real mono-germs of corank one and codimension one

Kevin Houston (2004)

Banach Center Publications

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Corank one mono-germs $f : (ℝ ⁿ, 0) \to (ℝ^{p}, 0)$ , n < p, of $_{e}$ -codimension one are classified by giving an explicit normal form.

A construction of a connection on $G Y \to Y$ from a connection on $Y \to M$ by means of classical linear connections on $M$ and $Y$

Włodzimierz M. Mikulski (2005)

Commentationes Mathematicae Universitatis Carolinae

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Let $G$ be a bundle functor of order $(r, s, q)$ , $s \geq r \leq q$ , on the category $ℱ ℳ_{m, n}$ of $(m, n)$ -dimensional fibered manifolds and local fibered diffeomorphisms. Given a general connection $Γ$ on an $ℱ ℳ_{m, n}$ -object $Y \to M$ we construct a general connection $𝒢 (Γ, λ, Λ)$ on $G Y \to Y$ be means of an auxiliary $q$ -th order linear connection $λ$ on $M$ and an $s$ -th order linear connection $Λ$ on $Y$ . Then we construct a general connection $𝒢 (Γ, \nabla_{1}, \nabla_{2})$ on $G Y \to Y$ by means of auxiliary classical linear connections $\nabla_{1}$ on $M$ and $\nabla_{2}$ on $Y$ . In the case $G = J^{1}$ we determine all general connections...

A discrete phenomenon in propagation of $C^{\infty}$ singularities

Paul Godin (1987)

Banach Center Publications

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Displaying similar documents to “Normal forms for certain singularities of vectorfields”

Holonomy groups of complete flat manifolds

A generalization of Thom’s transversality theorem

Simple singularities of multigerms of curves.

On the classification of real mono-germs of corank one and codimension one

A construction of a connection on G Y → Y from a connection on Y → M by means of classical linear connections on M and Y

A discrete phenomenon in propagation of C ∞ singularities

A construction of a connection on $G Y \to Y$ from a connection on $Y \to M$ by means of classical linear connections on $M$ and $Y$

A discrete phenomenon in propagation of $C^{\infty}$ singularities