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Statistical stability for multidimensional piecewise expanding maps


Authors: José F. Alves, Antonio Pumariño and Enrique Vigil
Journal: Proc. Amer. Math. Soc. 145 (2017), 3057-3068
MSC (2010): Primary 37A05, 37A10, 37C75
DOI: https://doi.org/10.1090/proc/13518
Published electronically: February 22, 2017
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Abstract: We present sufficient conditions for the (strong) statistical stability of some classes of multidimensional piecewise expanding maps. As a consequence we get that a certain natural two-dimensional extension of the classical one-dimensional family of tent maps is statistically stable.


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Additional Information

José F. Alves
Affiliation: Centro de Matemática da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
Email: jfalves@fc.up.pt

Antonio Pumariño
Affiliation: Departamento de Matemáticas, Facultad de Ciencias de la Universidad de Oviedo, Calvo Sotelo s/n, 33007 Oviedo, Spain
Email: apv@uniovi.es

Enrique Vigil
Affiliation: Departamento de Matemáticas, Facultad de Ciencias de la Universidad de Oviedo, Calvo Sotelo s/n, 33007 Oviedo, Spain
Email: vigilkike@gmail.com

DOI: https://doi.org/10.1090/proc/13518
Keywords: Piecewise expanding maps, physical measures, statistical stability
Received by editor(s): September 2, 2015
Received by editor(s) in revised form: August 25, 2016
Published electronically: February 22, 2017
Additional Notes: The first author was partially funded by Fundação Calouste Gulbenkian, by the European Regional Development Fund through the program COMPETE and by the Portuguese Government through FCT under the projects PEst-C/MAT/UI0144/2013 and PTDC/MAT/120346/2010
The second and third authors were partially supported by MEC grant MTM2011-22956 and MINECO-15-MTM2014-56953-P. The third author was also supported by the Foundation for the Promotion of Applied Scientific Research and Technology in Asturias (BP12-123) and by CMUP (UID/MAT/00144/2013), which is funded by FCT with national (MEC) and European structural funds through the programs FEDER, under the partnership agreement PT2020.
Communicated by: Nimish Shah
Article copyright: © Copyright 2017 American Mathematical Society