
Dynamics on the Space of Holomorphic Functions
Abdelghani Zeghib Ecole Normale Superieure de Lyon, France 

Abstract:
We study here the action of subgroups of PSL (2,R) on the
space of harmonic functions on the unit disc bounded by a common
constant, as well as the relationship this action has with the
foliated Liouville problem: Given a foliation of a compact
manifold by Riemannian leaves and a leafwise harmonic continuous
function on the manifold, is the function leafwise constant? We
give a number of positive results and also show a general class of
examples for which the Liouville property does not hold. The
connection between the Liouville property and the dynamics on the
space of harmonic functions as well as general properties of this
dynamical system are explored. It is shown among other properties
that the Zaction generated by hyperbolic or parabolic
elements of PSL (2,R) is chaotic.
Information:
Date: Saturday, February 8, 2003, 14:0015:00
Place: School of Mathematics, Niavaran Bldg., Niavaran Square, Tehran, Iran
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