Let F be a germ of holomorphic diffeomorphism of C-2 fixing O and such that dF(O) has eigenvalues 1 and e(itheta) with \e(itheta)\ = 1 and e(itheta) not equal 1. Introducing suitable normal forms for F we define an invariant, nu(F) greater than or equal to 2, and a generic condition, that of being dynamically separating. In the case F is dynamically separating, we prove that there exist nu(F) - 1 parabolic curves for F at O tangent to the eigenspace of 1.
Bracci, F., Molino, L. (2004). The dynamics near quasi-parabolic fixed points of holomorphic diffeomorphisms in C-2. AMERICAN JOURNAL OF MATHEMATICS, 126(3), 671-686.
The dynamics near quasi-parabolic fixed points of holomorphic diffeomorphisms in C-2
BRACCI, FILIPPO;
2004-01-01
Abstract
Let F be a germ of holomorphic diffeomorphism of C-2 fixing O and such that dF(O) has eigenvalues 1 and e(itheta) with \e(itheta)\ = 1 and e(itheta) not equal 1. Introducing suitable normal forms for F we define an invariant, nu(F) greater than or equal to 2, and a generic condition, that of being dynamically separating. In the case F is dynamically separating, we prove that there exist nu(F) - 1 parabolic curves for F at O tangent to the eigenspace of 1.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
bracci.pdf
accesso aperto
Licenza:
Creative commons
Dimensione
338.08 kB
Formato
Adobe PDF
|
338.08 kB | Adobe PDF | Visualizza/Apri |
Questo articolo è pubblicato sotto una Licenza Licenza Creative Commons