Hypercyclic operators for iterated function systems. (English) Zbl 1484.47017
Summary: In this paper, we introduce and study the notion of hypercyclicity for iterated function systems (IFS) of operators. We prove that for a linear IFS, hypercyclicity implies sensitivity and if an IFS is abelian, then hypercyclicity also implies multi-sensitivity and hence thick sensitivity. We also give some equivalent conditions for hypercyclicity as well as weakly mixing for an IFS of operators.
MSC:
| 47A16 | Cyclic vectors, hypercyclic and chaotic operators |
| 37B05 | Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
Keywords:
iterated function systems; hypercyclic operators; sensitive operators; weakly mixing operatorsReferences:
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