Displaying similar documents to “On divergent diagrams of finite codimension.”

Topological K-equivalence of analytic function-germs

Sérgio Alvarez, Lev Birbrair, João Costa, Alexandre Fernandes (2010)

Open Mathematics

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We study the topological K-equivalence of function-germs (ℝn, 0) → (ℝ, 0). We present some special classes of piece-wise linear functions and prove that they are normal forms for equivalence classes with respect to topological K-equivalence for definable functions-germs. For the case n = 2 we present polynomial models for analytic function-germs.

∞-jets of diffeomorphisms preserving orbits of vector fields

Sergiy Maksymenko (2009)

Open Mathematics

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Let F be a C ∞ vector field defined near the origin O ∈ ℝn, F(O) = 0, and (Ft) be its local flow. Denote by the set of germs of orbit preserving diffeomorphisms h: ℝn → ℝn at O, and let , (r ≥ 0), be the identity component of with respect to the weak Whitney Wr topology. Then contains a subset consisting of maps of the form Fα(x)(x), where α: ℝn → ℝ runs over the space of all smooth germs at O. It was proved earlier by the author that if F is a linear vector field, then = . In this paper...

Local reduction theorems and invariants for singular contact structures

Bronislaw Jakubczyk, Michail Zhitomirskii (2001)

Annales de l’institut Fourier

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A differential 1-form on a ( 2 k + 1 ) -dimensional manifolds M defines a singular contact structure if the set S of points where the contact condition is not satisfied, S = { p ∈ M : ( ω ∧ ( d ω ) k ( p ) = 0 } , is nowhere dense in M . Then S is a hypersurface with singularities and the restriction of ω to S can be defined. Our first theorem states that in the holomorphic, real-analytic, and smooth categories the germ of Pfaffian equation ( ω ) generated by ω is determined, up to a diffeomorphism, by its restriction to S , if we eliminate...