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Invariant densities and escape rates: rigorous and computable approximations in the L[infinity]-norm

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journal contribution
posted on 01.09.2017, 08:51 by Wael Bahsoun, Christopher Bose
In this article, we study piecewise linear discretization schemes for transfer operators (PerronFrobenius operators) associated with interval maps. We show how these can be used to provide rigorous pointwise approximations for invariant densities of Markov interval maps. We also derive the order of convergence of the approximate invariant density to the real one in the L ∞ -norm. The outcome of this paper complements recent results on the formulae of escape rates of open dynamical systems, (Keller and Liverani, 2009) [7]. In particular, the novelty of our work over previous results on BV and L ∞ approximations is that it provides a method for explicit computation of the approximation error.

Funding

CB is supported by an NSERC grant.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Nonlinear Analysis, Theory, Methods and Applications

Volume

74

Issue

13

Pages

4481 - 4495

Citation

BAHSOUN, W. and BOSE, C., 2011. Invariant densities and escape rates: rigorous and computable approximations in the L[infinity]-norm. Nonlinear Analysis: Theory, Methods and Applications, 74 (13), pp.4481-4495.

Publisher

© Elsevier

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

2011

ISSN

0362-546X

Language

en

Exports

Loughborough Publications

Keywords

Exports