Linear transitivity criteria. (English) Zbl 1099.47005
The authors recall some known transitivity criteria, they introduce a new transitivity criterion in terms of the existence of suitable backward orbits, and they show their equivalence with the property of weakly mixing. They also characterize weakly mixing invertible operators with an easy computable condition. Furthermore, they introduce new transitivity criteria for semigroups (semiflows) of operators inspired by the correspondiug discrete version and show their equivalence with weakly mixing.
Reviewer: Bahman Yousefi (Shiraz)
MSC:
| 47A16 | Cyclic vectors, hypercyclic and chaotic operators |
| 37C10 | Dynamics induced by flows and semiflows |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 47D06 | One-parameter semigroups and linear evolution equations |
| 54H20 | Topological dynamics (MSC2010) |
Keywords:
cyclic vectors; hypercyclic vectors; topological transitivity; semigroups of operators; weakly mixing; chaosReferences:
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