On compositional dynamics on spaces of analytic functions. (English) Zbl 1519.47008
This article investigates super-recurrence, super-rigidity, and uniformly super-rigidity of composition operators \(C_\varphi\) acting on the space of holomorphic functions on the complex plane or on the punctured plane. These classes of composition operators are characterized in terms of the symbol \(\varphi\).
Reviewer: José Bonet (València)
MSC:
| 47A16 | Cyclic vectors, hypercyclic and chaotic operators |
| 47B33 | Linear composition operators |
| 37B20 | Notions of recurrence and recurrent behavior in topological dynamical systems |
| 46E50 | Spaces of differentiable or holomorphic functions on infinite-dimensional spaces |
| 46T25 | Holomorphic maps in nonlinear functional analysis |
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