Delays, Recurrence and Ordinals |
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Authors: | Mathias A. R. D. |
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Affiliation: | Universidad de los Andes AA4976 Santa Fe de Bogotá, Colombia |
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Abstract: | We apply set-theoretical ideas to an iteration problem of dynamicalsystems. Among other results, we prove that these iterationsnever stabilise later than the first uncountable ordinal; forevery countable ordinal we give examples in Baire space andin Cantor space of an iteration that stabilises exactly at thatordinal; we give an example of an iteration with recursive datawhich stabilises exactly at the first non-recursive ordinal;and we find new examples of complete analytic sets simply definablefrom concepts of recurrence. 2000 Mathematics Subject Classification:primary 03E15, 37B20, 54H05; secondary 37B10, 37E15. |
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Keywords: | Polish space iterated continuous function orbit limit point the attacking relation recurrent point well-founded relation analytic set ordinal |
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