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Rigorous pointwise approximations for invariant densities of non-uniformly expanding maps

Published online by Cambridge University Press:  10 January 2014

WAEL BAHSOUN ,
CHRISTOPHER BOSE  and
YUEJIAO DUAN
WAEL BAHSOUN
Affiliation:
Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK email W.Bahsoun@lboro.ac.ukY.Duan@lboro.ac.uk
CHRISTOPHER BOSE
Affiliation:
Department of Mathematics and Statistics, University of Victoria, PO Box 3045 STN CSC, Victoria, BC, V8W 3R4, Canada email cbose@uvic.ca
YUEJIAO DUAN
Affiliation:
Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK email W.Bahsoun@lboro.ac.ukY.Duan@lboro.ac.uk
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Abstract

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We use an Ulam-type discretization scheme to provide pointwise approximations for invariant densities of interval maps with a neutral fixed point. We prove that the approximate invariant density converges pointwise to the true density at a rate ${C}^{\ast } \cdot (\ln m)/ m$, where ${C}^{\ast } $ is a computable fixed constant and ${m}^{- 1} $ is the mesh size of the discretization.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 4 , June 2015 , pp. 1028 - 1044
Copyright
© Cambridge University Press, 2014 

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