Let F be a germ of analytic transformation of (Cp, 0). We say that F is semi-attractive at the origin, if F'(0) has one eigenvalue equal to 1 and if the other ones are of modulus strictly less than 1. The main result is: either there exists a curve of fixed points, or F - Id has multiplicity k and there exists a domain of attraction with k - 1 petals. We also study the case where F is a global isomorphism of C2 and F - Id has multiplicity k at the origin. This work has been inspired by two papers: one of P. Fatou (1924) and the other one of T. Ueda (1986).
@article{urn:eudml:doc:41174,
title = {Attracting domains for semi-attractive transformations of Cp.},
journal = {Publicacions Matem\`atiques},
volume = {38},
year = {1994},
pages = {479-499},
mrnumber = {MR1316642},
zbl = {0832.58031},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41174}
}
Hakim, Monique. Attracting domains for semi-attractive transformations of Cp.. Publicacions Matemàtiques, Tome 38 (1994) pp. 479-499. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41174/