Gobbino, Massimo and Simon, Robert Samuel
(2009)
*How many times can a function be iterated?*
arXiv.

## Abstract

Let C be a closed subset of a topological space X, and let f : C --> X. Let us assume that f is continuous and f(x) lies in C for every x in the boundary of C. How many times can one iterate f? This paper provides estimates on the number of iterations and examples of their optimality. In particular we show how some topological properties of f, C, X are related to the maximal number of iterations, both in the case of functions and in the more general case of set-valued maps.

Item Type: | Monograph (Other) |
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Official URL: | http://arxiv.org/ |

Additional Information: | © 2009 The authors |

Library of Congress subject classification: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Rights: | http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx |

Date Deposited: | 09 Apr 2010 13:14 |

URL: | http://eprints.lse.ac.uk/27682/ |

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