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Article: Algebraic periods of self-maps of a rational exterior space of rank 2.
- Article from:
- Fixed Point Theory and Applications
- Article date:
- January 1, 2006
- Author:
CopyrightCOPYRIGHT 2006 Hindawi Publishing Corp. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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The paper presents a complete description of the set of algebraic periods for self-maps of a rational exterior space which has rank 2.
1. Introduction
A natural number m is called a minimal period of a map f if f m has a fixed point which is not fixed by any earlier iterates. One important device for studying minimal periods are the integers [i.sub.m](f) = [[summation].sub.k/m] [mu](m/k)L([f.sup.k]), where L([f.sup.k]) denotes the Lefschetz number of [f.sup.k] and [mu] is the classical Mobius function. If [i.sub.m] (f) [not equal to] 0, then we say that m is an algebraic period of f . In many cases the fact that m is an algebraic period provides ...