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Sharkovskii's theorem for multidimensional perturbations of one-dimensional maps

Published online by Cambridge University Press:  01 December 1999

PIOTR ZGLICZYŃSKI
PIOTR ZGLICZYŃSKI
Affiliation:
Jagiellonian University, Institute of Mathematics, Reymonta 4, 30-059 Kraków, Poland (e-mail: [email protected]) Current address: Center of Dynamical Systems and Nonlinear Studies, School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA (e-mail: [email protected]).
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Abstract

We present Sharkovskii's theorem for multidimensional perturbations of one-dimensional maps. We show that if an unperturbed one-dimensional map has a point of period $n$, then sufficiently close multidimensional perturbations of this map have periodic points of all periods which are allowed by Sharkovskii's theorem.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 19 , Issue 6 , December 1999 , pp. 1655 - 1684
Copyright
1999 Cambridge University Press

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