Dynamical properties for composition operators on $H^2({\mathbb{C}}_{+})$

Abstract

Expansivity, Li-Yorke chaos and shadowing are popular and well-studied notions of dynamical systems. Several simple and useful characterizations of these notions within the setting of linear dynamics were obtained recently. We explore these three dynamical properties for composition operators $C_{\varphi }f=f\circ \varphi$ induced by affine self-maps $\varphi$ of the right half-plane ${\mathbb{C}}_{+}$ on the Hardy-Hilbert space $H^2({\mathbb{C}}_{+})$.

arXiv comment10 pages. We fixed the proof of the Theorem 7, in its last version there is a mistake with the density of the kernels

References in corpus (5)

• Linear dynamical systems on Hilbert spaces: typical properties and explicit examples
• Composition operators on Hardy spaces of a half plane
• Li-Yorke Chaos for Composition Operators on $L^p$-Spaces
• Spectra of linear fractional composition operators on the Hardy and weighted Bergman spaces of the half-plane
• Complex symmetry of linear fractional composition operators on a half-plane

Cited by in corpus (1)

• Dynamics for affine composition operators on weighted Bergman space of a half plane