Complex dynamical systems and the geometry of domains in Banach spaces

Mark Elin, Simeon Reich, and David Shoikhet. Complex dynamical systems and the geometry of domains in Banach spaces. 2004. <http://eudml.org/doc/285979>.

@book{MarkElin2004,
abstract = {We consider semigroups of holomorphic self-mappings on domains in Hilbert and Banach spaces, and then develop a new dynamical approach to the study of geometric properties of biholomorphic mappings. We establish, for example, several flow invariance conditions and find parametric representations of semicomplete vector fields. In order to examine the asymptotic behavior of these semigroups, we use diverse tools such as hyperbolic metric theory and estimates of solutions of generalized differential equations. In addition, we introduce a new method involving admissible upper and lower bounds. Finally, we apply our dynamical approach to obtain several growth and covering theorems for star-like mappings on the open unit balls of Banach and Hilbert spaces.},
author = {Mark Elin, Simeon Reich, David Shoikhet},
keywords = {asymptotic behavior; complete and semicomplete vector fields; holomorphic generators; growth and covering theorems; nonlinear semigroups; star-like mappings; spiral-like mappings},
language = {eng},
title = {Complex dynamical systems and the geometry of domains in Banach spaces},
url = {http://eudml.org/doc/285979},
year = {2004},
}

TY - BOOK
AU - Mark Elin
AU - Simeon Reich
AU - David Shoikhet
TI - Complex dynamical systems and the geometry of domains in Banach spaces
PY - 2004
AB - We consider semigroups of holomorphic self-mappings on domains in Hilbert and Banach spaces, and then develop a new dynamical approach to the study of geometric properties of biholomorphic mappings. We establish, for example, several flow invariance conditions and find parametric representations of semicomplete vector fields. In order to examine the asymptotic behavior of these semigroups, we use diverse tools such as hyperbolic metric theory and estimates of solutions of generalized differential equations. In addition, we introduce a new method involving admissible upper and lower bounds. Finally, we apply our dynamical approach to obtain several growth and covering theorems for star-like mappings on the open unit balls of Banach and Hilbert spaces.
LA - eng
KW - asymptotic behavior; complete and semicomplete vector fields; holomorphic generators; growth and covering theorems; nonlinear semigroups; star-like mappings; spiral-like mappings
UR - http://eudml.org/doc/285979
ER -