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DELAYS, RECURRENCE AND ORDINALS

Published online by Cambridge University Press:  05 March 2001

A. R. D. MATHIAS
A. R. D. MATHIAS
Affiliation:
Universidad de los Andes, AA4976 Santa Fe de Bogotá, Colombia Present address: Département de Mathématiques et Informatique, Université de la Réunion, 15, Avenue René Cassin, BP 7151, F 97715 St Denis de la Réunion, Messagerie 9, France outre-mer ardm@univ-reunion.fr
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Abstract

We apply set-theoretical ideas to an iteration problem of dynamical systems. Among other results, we prove that these iterations never stabilise later than the first uncountable ordinal; for every countable ordinal we give examples in Baire space and in Cantor space of an iteration that stabilises exactly at that ordinal; we give an example of an iteration with recursive data which stabilises exactly at the first non-recursive ordinal; and we find new examples of complete analytic sets simply definable from concepts of recurrence.

2000 Mathematics Subject Classification: primary 03E15, 37B20, 54H05; secondary 37B10, 37E15.

Keywords

Polish spaceiterated continuous functionorbit limit pointthe attacking relationrecurrent pointwell-founded relationanalytic setordinal
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 82 , Issue 2 , March 2001 , pp. 257 - 298
Copyright
2001 London Mathematical Society

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