Hypercyclic composition operators on spaces of real analytic functions

Source abstract

Abstract We study the dynamical behaviour of composition operators C ϕ defined on spaces (Ω) of real analytic functions on an open subset Ω 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 ϕ is a self map on a simply connected complex neighbourhood U of ℝ, U ≠ ℂ, then topological transitivity, hypercyclicity and sequential hypercyclicity of C ϕ : (ℝ) → (ℝ) are equivalent.