Observable Optimal State Points of Sub-additive Potentials
Abstract
For a sequence of sub-additive potentials, Dai [Optimal state points of the sub-additive ergodic theorem, Nonlinearity, 24 (2011), 1565-1573] gave a method of choosing state points with negative growth rates for an ergodic dynamical system. This paper generalizes Dai's result to the non-ergodic case, and proves that under some mild additional hypothesis, one can choose points with negative growth rates from a positive Lebesgue measure set, even if the system does not preserve any measure that is absolutely continuous with respect to Lebesgue measure.
Keywords
Cite
@article{arxiv.1109.6710,
title = {Observable Optimal State Points of Sub-additive Potentials},
author = {Eleonora Catsigeras and Yun Zhao},
journal= {arXiv preprint arXiv:1109.6710},
year = {2013}
}
Comments
16 pages. This work was reported in the summer school in Nanjing University. In this second version we have included some changes suggested by the referee. The final version will appear in Discrete and Continuous Dynamical Systems- Series A - A.I.M. Sciences and will be available at http://aimsciences.org/journals/homeAllIssue.jsp?journalID=1