Note on a Poincaré map
Michal Fečkan (1991)
Mathematica Slovaca
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Michal Fečkan (1991)
Mathematica Slovaca
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Włodzimierz Waliszewski (1985)
Časopis pro pěstování matematiky
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P. Michor (1980)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Sergei A. Dovbysh (1999)
Collectanea Mathematica
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It is well-known that the existence of transversally intersecting separatrices of hyperbolic periodic solutions leads, in a typical situation, to complicated and irregular dynamics. Therefore, in the case of a two-dimensional mapping or a three-dimensional flow, with this transversality property, there is no non-trivial analytic or meromorphic first integral, i.e., a function constant along each trajectory of the system under consideration. Additional robust conditions are obtained and...
P. Michor (1983)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Ciampa, S.
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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...