Ergodic Theory and Dynamical Systems

Table of Contents - 2006 - Volume 26, Issue 05  


A geometric characterization of linear hyperbolic flows on $\mathbb{C}^n$

TOSHIKAZU ITO a1 and BRUNO SCÁRDUA a2
a1 Department of Natural Science, Ryukoku University, Fushimi-ku, Kyoto 612, Japan
a2 Instituto Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21.945-970 Rio de Janeiro-RJ, Brazil (e-mail: scardua@impa.br)

Article author query
ito t   [Google Scholar] 
scardua b   [Google Scholar] 
 

Abstract

We prove that a polynomial vector field on $\mathbb{C}^n$, $n\geq 2$, whose corresponding projective foliation has only singularities of hyperbolic type is linear in some affine chart provided that it is transverse to a sequence of spheres bounding balls exhausting ${\mathbb{C}}^n$.

(Published Online July 26 2006)
(Received April 2 2005)
(Accepted February 28 2006)