Pregled bibliografske jedinice broj: 1124633
On the Universal Unfolding of Vector Fields in One Variable: A Proof of Kostov’s Theorem
On the Universal Unfolding of Vector Fields in One Variable: A Proof of Kostov’s Theorem // Qualitative Theory of Dynamical Systems, 19 (2020), 3; 80, 13 doi:10.1007/s12346-020-00416-y (međunarodna recenzija, članak, znanstveni)
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Naslov
On the Universal Unfolding of Vector Fields in One Variable: A Proof of Kostov’s Theorem
Autori
Klimeš, Martin ; Rousseau, Christiane
Izvornik
Qualitative Theory of Dynamical Systems (1575-5460) 19
(2020), 3;
80, 13
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
normal forms of analytic vector fields ; unfolding of singularities ; versal deformations
Sažetak
In 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 C-infinity case, where we show that only versality is possible.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
Citiraj ovu publikaciju:
Časopis indeksira:
- Current Contents Connect (CCC)
- Web of Science Core Collection (WoSCC)
- Science Citation Index Expanded (SCI-EXP)
- SCI-EXP, SSCI i/ili A&HCI
- Scopus
