Disjoint hypercyclic and supercyclic composition operators.
by
Ozgur Martin
Bowling Green State University
Coauthors: Juan P. Bes

We say a sequence of linear continuous operators (T_n) on a topological vector space X is hypercyclic (resp. supercylic) if there exists an element x in X such that the orbit {T_n(x) : n ≥ 0} (resp. the projective orbit {cT_n(x) : n ≥ 0, c ∈ C}) is dense in X. When X is the set of holomorphic functions on a simply connected domain, Bernal, Bonilla, and Calderon showed that for most sequences of composition operators induced by automorphic symbols the notions of hypercyclicity and supercyclicity coincide. In this talk, we will show that this result holds for all sequences and also can be generalized to the notion of disjointness in hypercyclicity introduced by Bernal and also independently by Bes and Peris.

Date received: January 20, 2010