Hypercyclic composition operators on spaces of real analytic functions

We study the dynamical behaviour of composition operators C. defined on spaces A (Omega) of real analytic functions on an open subset Omega of R-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 R, U (sic) C, then topological transitivity, hypercyclicity and sequential hypercyclicity of C-phi : A (R) -> A (R) are equivalent.