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

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posted on 25.05.2016, 13:39 by Wael BahsounWael Bahsoun, Christopher Bose, Yuejiao Duan
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∗⋅(lnm)/m, where C∗ is a computable fixed constant and m−1 is the mesh size of the discretization.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

ERGODIC THEORY AND DYNAMICAL SYSTEMS

Volume

35

Pages

1028 - 1044 (17)

Citation

BAHSOUN, W., BOSE, C. and DUAN, Y., 2015. Rigorous pointwise approximations for invariant densities of non-uniformly expanding maps. Ergodic Theory and Dynamical Systems, 35 (4), pp. 1028 - 1044.

Publisher

© Cambridge University Press

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2015

Notes

This article was published in the journal Ergodic Theory and Dynamical Systems and the definitive version is available at: http://dx.doi.org/10.1017/etds.2013.91

ISSN

0143-3857

Language

en

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