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2009 | 7 | 2 | 272-298
Tytuł artykułu

∞-jets of diffeomorphisms preserving orbits of vector fields

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 we present a class of examples of vector fields with degenerate singularities at O for which formally coincides with , i.e. on the level of ∞-jets at O. We also establish parameter rigidity of linear vector fields and “reduced” Hamiltonian vector fields of real homogeneous polynomials in two variables.
Wydawca
Czasopismo
Rocznik
Tom
7
Numer
2
Strony
272-298
Opis fizyczny
Daty
wydano
2009-06-01
online
2009-05-24
Twórcy
  • Topology Department, Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine, maks@imath.kiev.ua
Bibliografia
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-009-0010-y
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