Abstract
We study the dynamical behaviour of composition operators C ¿ defined on spaces A(¿) of real analytic functions on an open subset ¿ of ¿ d. We characterize when such operators are topologically transitive, i.e. when for every pair of non-empty open sets there is an orbit intersecting both of them. Moreover, under mild assumptions on the composition operator, we investigate when it is sequentially hypercyclic, i.e., when it has a sequentially dense orbit. If ¿ is a self map on a simply connected complex neighbourhood U of ¿, U ¿ ¿, then topological transitivity, hypercyclicity and sequential hypercyclicity of C ¿: A(¿) ¿ A(¿) are equivalent. © 2012 Cambridge Philosophical Society.
