Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-27T08:16:20.309Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)