Algebraic foliations defined by complete vector fields

2011 ◽  
Vol 94 ◽  
pp. 143-151
Author(s):  
Alvaro Bustinduy
Keyword(s):  
Vector Fields ◽  
Complete Vector ◽  
Complete Vector Fields ◽  
Algebraic Foliations

scholarly journals COMPLETE VECTOR FIELDS ON ℂ2 WHOSE UNDERLYING FOLIATION IS POLYNOMIAL

2010 ◽  
Vol 21 (03) ◽  
pp. 333-347 ◽  
Author(s):  
ALVARO BUSTINDUY
Keyword(s):  
Vector Fields ◽  
Complex Variables ◽  
Polynomial Vector ◽  
Polynomial Vector Fields ◽  
Complete Vector ◽  
Complete Vector Fields

We extend the classification of complete polynomial vector fields in two complex variables given by Brunella to cover the case of holomorphic (non-polynomial) vector fields whose underlying foliation is still polynomial.

scholarly journals Generation theory for semigroups of holomorphic mappings in Banach spaces

1996 ◽  
Vol 1 (1) ◽  
pp. 1-44 ◽  
Author(s):  
Simeon Reich ◽  
David Shoikhet
Keyword(s):  
Banach Spaces ◽  
Vector Fields ◽  
Spectral Characteristics ◽  
Point Theory ◽  
Null Point ◽  
Holomorphic Mappings ◽  
Convex Domains ◽  
Open Problems ◽  
Nonlinear Semigroups ◽  
Complete Vector

We study nonlinear semigroups of holomorphic mappings in Banach spaces and their infinitesimal generators. Using resolvents, we characterize, in particular, bounded holomorphic generators on bounded convex domains and obtain an analog of the Hille exponential formula. We then apply our results to the null point theory of semi-plus complete vector fields. We study the structure of null point sets and the spectral characteristics of null points, as well as their existence and uniqueness. A global version of the implicit function theorem and a discussion of some open problems are also included.

Sign in / Sign up

Export Citation Format

Share Document