Full cascades of simple periodic orbits on the interval
Any continuous interval map of type greater than 2∞ is shown to have what we call a full cascade of simple periodic orbits. This is used to prove that, for maps of any types, the existence of such a full cascade is equivalent to the existence of an infinite ω-limit set. For maps of type 2∞, this is...
Gespeichert in:
| Datum: | 1996 |
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| Hauptverfasser: | , |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
1996
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| Schriftenreihe: | Український математичний журнал |
| Schlagworte: | |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/156038 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Full cascades of simple periodic orbits on the interval / López V. Jiménez, L. Snoha // Український математичний журнал. — 1996. — Т. 48, № 12. — С. 1628–1637. — Бібліогр.: 16 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Any continuous interval map of type greater than 2∞ is shown to have what we call a full cascade of simple periodic orbits. This is used to prove that, for maps of any types, the existence of such a full cascade is equivalent to the existence of an infinite ω-limit set. For maps of type 2∞, this is equivalent to the existence of a (period doubling) solenoid. Hence, any map of type 2∞ which is either piecewise monotone (with finite number of pieces) or continuously differentiable has both a full cascade of simple periodic orbits and a solenoid. |
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