The iterates of a map with dense orbit
Let / : X —» X be a continuous map on a Hausdorff topological space X without isolated points. We show that if the orbit of a point x e X under / is dense in X while the orbit of x under fN,N > 1, is not, then the space X decomposes into a family of sets relative to which the behaviour of / is si...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2008
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| Sorozat: | Acta scientiarum mathematicarum
74 No. 1-2 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16237 |
| Tartalmi kivonat: | Let / : X —» X be a continuous map on a Hausdorff topological space X without isolated points. We show that if the orbit of a point x e X under / is dense in X while the orbit of x under fN,N > 1, is not, then the space X decomposes into a family of sets relative to which the behaviour of / is simple to describe. This decomposition solves a problem that P. S. Bourdon posed in 1996 ([3]). A slight variant of our result also provides a new argument for the celebrated theorem of S. Ansari [1]: If T is a hypercyclic operator on a topological vector space X then T and TN have the same sets of hypercyclic vectors (N > 1). |
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| Terjedelem/Fizikai jellemzők: | 245-257 |
| ISSN: | 0001-6969 |