Holomorphic foliations  transverse to manifolds with corners

Toshikazu Ito; Bruno Scárdua

doi:10.3934/dcds.2009.25.537

Article Contents

2009, Volume 25, Issue 2: 537-544. Doi: 10.3934/dcds.2009.25.537

This issue Previous Article Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation Next Article A variational inequality in Bean's model for superconductors with displacement current

Holomorphic foliations transverse to manifolds with corners

Toshikazu Ito¹ and
Bruno Scárdua^2,

1.
Department of Natural Science - Ryukoku University, Fushimi-Ku, Kyoto 612
2.
Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21.945-970, Rio de Janeiro, RJ

Received: May 31, 2008

Revised: November 30, 2008

Published: May 2009

Abstract Related Papers Cited by

Abstract

We study the geometrical and dynamical properties of a holomorphic vector field on a complex surface, assumed to be transverse to the boundary of a domain which is a non-smooth manifold with boundary and corners. We obtain hyperbolicity and prove a compact leaf result. For a pseudoconvex domain with boundary diffeomorphic to the boundary of a bidisc in $\mathbb C^2$ the foliation is pull-back of a liner hyperbolic foliation. If moreover the diffeomorphism is transversely holomorphic then we have linearization.

Keywords:

Mathematics Subject Classification: Primary: 37F75; Secondary: 32M25, 32S65.

Citation:

Article Metrics

HTML views() PDF downloads(193) Cited by(0)

Holomorphic foliations transverse to manifolds with corners

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Holomorphic foliations transverse to manifolds with corners

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content