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Invariant densities and escape rates: rigorous and computable approximations in the L[infinity]-norm
journal contribution
posted on 2017-09-01, 08:51 authored by Wael BahsounWael Bahsoun, Christopher BoseIn 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 ApplicationsVolume
74Issue
13Pages
4481 - 4495Citation
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
© ElsevierVersion
- 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
2011ISSN
0362-546XPublisher version
Language
- en