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

Published online by Cambridge University Press:  26 July 2006

TOSHIKAZU ITO  and
BRUNO SCÁRDUA
TOSHIKAZU ITO
Affiliation:
Department of Natural Science, Ryukoku University, Fushimi-ku, Kyoto 612, Japan
BRUNO SCÁRDUA
Affiliation:
Instituto Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21.945-970 Rio de Janeiro-RJ, Brazil (e-mail: scardua@impa.br)
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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 ${\mathbb{C}}^n$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 5 , October 2006 , pp. 1569 - 1578
Copyright
2006 Cambridge University Press

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