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Ergodic and algebraic properties for dynamical systems which preserves an infinite measure

Grant number: 11/11663-5
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): September 01, 2011
Effective date (End): September 09, 2015
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Ali Messaoudi
Grantee:Patricia Romano Cirilo
Home Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
Associated research grant:08/02841-4 - Topology, geometry and ergodic theory of dynamical systems, AP.TEM
Associated scholarship(s):13/16553-9 - Ergodic and algebraic properties for dynamical systems which preserves an infinite measure: the elliptic dynamics context, BE.EP.PD


This project aims to study ergodic and algebraic properties for a class of dynamical systems whose invariant measure is infinite. It is noteworthy that the classical Birkhoff ergodic theorem is not valid when the measure preserved by the system is not finite. We will study skew products defined on cylinders whose base is minimal, for example irrational rotations on the n-dimensional torus. Topics to be covered include ergodic theorems, asymptotic behavior of ergodic sums, return sequences, limits on distribution and Rauzy fractals of Diophantine approximations. (AU)

Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
BERNARDES, JR., NILSON C.; CIRILO, PATRICIA R.; DARJI, UDAYAN B.; MESSAOUDI, ALI; PUJALS, ENRIQUE R. Expansivity and shadowing in linear dynamics. Journal of Mathematical Analysis and Applications, v. 461, n. 1, p. 796-816, MAY 1 2018. Web of Science Citations: 5.
CIRILO, PATRICIA; LIMA, YURI; PUJALS, ENRIQUE. Ergodic properties of skew products in infinite measure. Israel Journal of Mathematics, v. 214, n. 1, p. 43-66, JUL 2016. Web of Science Citations: 0.

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