Observable Optimal State Points of Sub-additive Potentials

Details Observable Optimal State Points of Sub-additive Potentials Observable Optimal State Points of Sub-additive Potentials

2011-09-30

arxiv.org/abs/1109.6710v1

Mathematics

Dynamical Systems

17pages, this work was reported in the summer school in Nanjing University

Scientific paper

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 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.

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