Simon, Robert
(2007)
*How many times can a function be iterated?*
LSE-CDAM-2007-10.
London School of Economics and Political Science, London, UK.

## 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) ∈ C for every x ∈ ∂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 (Report) |
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Official URL: | http://www.cdam.lse.ac.uk/Reports/ |

Additional Information: | © 2007 London School of Economics and Political Science |

Library of Congress subject classification: | H Social Sciences > H Social Sciences (General) |

Sets: | Departments > Mathematics Research centres and groups > Computational, Discrete and Applicable Mathematics@LSE (CDAM) |

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

Identification Number: | LSE-CDAM-2007-10 |

Date Deposited: | 11 Jul 2008 11:47 |

URL: | http://eprints.lse.ac.uk/6900/ |

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