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Self-generation of self-replicating maps of an interval

Published online by Cambridge University Press:  19 September 2008

William Parry
William Parry*
Affiliation:
From the Mathematics Institute, University of Warwick, England
*
†Address for correspondence: Professor William Parry, Mathematics Institute, University of Warwick, Coventry CV4 7AL, England.
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Abstract

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We construct C1 symmetric maps of [−1, 1] to itself, satisfying a condition similar to Feigenbaum's: -φ(x) = φ(-x), φ2(bx) = bφ(x), 0<b <1. Under certain conditions, the non-wandering set consists of the one-sided Morse minimal set together with 2n points of period 2n for each n = 1, 2, … The main significance of the construction is its simplicity. Given a certain piece of the map φ, the rest is generated by the required equation.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 1 , Issue 2 , June 1981, pp. 197 - 208
Copyright
Copyright © Cambridge University Press 1981

References

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