Real-Formal Orbital Rigidity for Germs of Real Analytic Vector Fields on the Real Plane

2016 ◽  
Vol 23 (1) ◽  
pp. 89-109 ◽  
Author(s):  
Jessica Angélica Jaurez-Rosas
Keyword(s):  
Vector Fields ◽  
Real Plane ◽  
Analytic Vector ◽  
The Real ◽  
Real Analytic

scholarly journals Quasianalytic Ilyashenko Algebras

2018 ◽  
Vol 70 (1) ◽  
pp. 218-240 ◽  
Author(s):  
Patrick Speissegger
Keyword(s):  
Power Series ◽  
Asymptotic Expansions ◽  
Vector Fields ◽  
Analytic Vector ◽  
Generalized Power Series ◽  
Real Functions ◽  
Real Analytic

AbstractWe construct a quasianalytic field of germs at +∞ of real functions with logarithmic generalized power series as asymptotic expansions, such that is closed under differentiation and log-composition; in particular, is a Hardy field. Moreover, the field o (−log) of germs at 0+ contains all transition maps of hyperbolic saddles of planar real analytic vector fields.

scholarly journals On the Universal Unfolding of Vector Fields in One Variable: A Proof of Kostov’s Theorem

2020 ◽  
Vol 19 (3) ◽  
Author(s):  
Martin Klimeš ◽  
Christiane Rousseau
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Versal Deformation ◽  
Dimensional Vector ◽  
Universal Unfolding ◽  
Parabolic Point ◽  
The Real ◽  
Real Analytic

AbstractIn this note we present variants of Kostov’s theorem on a versal deformation of a parabolic point of a complex analytic 1-dimensional vector field. First we provide a self-contained proof of Kostov’s theorem, together with a proof that this versal deformation is indeed universal. We then generalize to the real analytic and formal cases, where we show universality, and to the $${\mathcal {C}}^\infty $$ C ∞ case, where we show that only versality is possible.

scholarly journals Lie Algebras of Vector Fields in the Real Plane

1992 ◽  
Vol s3-64 (2) ◽  
pp. 339-368 ◽  
Author(s):  
Artemio González-López ◽  
Niky Kamran ◽  
Peter J. Olver
Keyword(s):  
Lie Algebras ◽  
Vector Fields ◽  
Real Plane ◽  
The Real
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