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ON SUMMABILITY CONDITIONS FOR INTERVAL MAPS

Part of: Low-dimensional dynamical systems

Published online by Cambridge University Press:  13 June 2013

HUAIBIN LI
HUAIBIN LI*
Affiliation:
School of Mathematics and Information Science, Henan University, Kaifeng 475004, PR China
*
[email protected]
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Abstract

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Consider a map of class ${C}^{3} $ with nonflat critical points and with all periodic points hyperbolic repelling. We show that the ‘backward contracting condition’ implies the summability condition. This result is the converse of Theorem 3 of Bruin et al. [‘Large derivatives, backward contraction and invariant densities for interval maps’, Invent. Math. 172 (2008), 509–533].

Keywords

interval mapssummability conditionbackward contracting

MSC classification

Secondary: 37E05: Maps of the interval (piecewise continuous, continuous, smooth)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 2 , April 2014 , pp. 308 - 315
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

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