We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Hypercyclic composition operators on spaces of real analytic functions.
- Authors
BONET, JOSÉ; DOMAŃSKI, PAWEŁ
- Abstract
We study the dynamical behaviour of composition operators Cϕ defined on spaces (Ω) of real analytic functions on an open subset Ω of ℝd. 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 Cϕ:(ℝ) → (ℝ) are equivalent.
- Subjects
COMPOSITION operators; REAL analysis (Mathematics); ANALYTIC functions; TOPOLOGICAL transformation groups; MATHEMATICAL mappings
- Publication
Mathematical Proceedings of the Cambridge Philosophical Society, 2012, Vol 153, Issue 3, p489
- ISSN
0305-0041
- Publication type
Article
- DOI
10.1017/S0305004112000266