20 research outputs found
Index theorems for holomorphic self-maps
Let be a complex manifold and a (possibly singular)
subvariety of . Let be a holomorphic map such that
restricted to is the identity. We show that one can associate to a
holomorphic section of a sheaf related to the embedding of in and
that such a section reads the dynamical behavior of along . In
particular we prove that under generic hypotheses the canonical section
induces a holomorphic action in the sense of Bott on the normal bundle of (the
regular part of) in and this allows to obtain for holomorphic self-maps
with non- isolated fixed points index theorems similar to Camacho-Sad,
Baum-Bott and variation index theorems for holomorphic foliations. Finally we
apply our index theorems to obtain information about topology and dynamics of
holomorphic self-maps of surfaces with a compact curve of fixed points.Comment: 46 pages, published versio
Parabolic curves in ℂ3
We discuss a family of holomorphic self-maps of ℂ3 tangent to the identity at the origin presenting dynamical phenomena not appearing for lower-dimensional maps