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Invariant measures for maps of the interval that do not have points of some period

Published online by Cambridge University Press:  19 September 2008

Jozef Bobok  and
Milan Kuchta
Jozef Bobok
Affiliation:
KM FSv. ČVUT, Thákurova 7, 166 29 Praha 6, Czech Republic
Milan Kuchta
Affiliation:
Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovak Republic†
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Abstract

We study invariant measures for a continuous function which maps a real interval into itself. We show that the ratio of the measures of the two subintervals into which it is divided by a fixed point is constrained by the the set of periods of periodic points. As a consequence of this we give a new forcing relation between periodic points.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 14 , Issue 1 , March 1994 , pp. 9 - 21
Copyright
Copyright © Cambridge University Press 1994

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References

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