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Metastability of certain intermittent maps

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journal contribution
posted on 01.09.2017 by Wael Bahsoun, Sandro Vaienti
We study an intermittent map which has exactly two ergodic invariant densities. The densities are supported on two subintervals with a common boundary point. Due to certain perturbations, leakage of mass through subsets, called holes, of the initially invariant subintervals occurs and forces the subsystems to merge into one system that has exactly one invariant density. We prove that the invariant density of the perturbed system converges in the L1-norm to a particular convex combination of the invariant densities of the intermittent map. In particular, we show that the ratio of the weights in the combination is equal to the limit of the ratio of the measures of the holes.

Funding

S.V. was supported by the ANR-grant Perturbations.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Nonlinearity

Volume

25

Issue

1

Pages

107 - 124 (17)

Citation

BAHSOUN, W. and VAIENTI, S., 2012. Metastability of Certain Intermittent Maps. Nonlinearity, 25 (1), pp.107-124.

Publisher

© IOP and London Mathematical Society

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

2012

ISSN

0951-7715

eISSN

1361-6544

Language

en

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