Some Large Deviation Results for Dynamical Systems

@inproceedings{Young2010SomeLD,
  title={Some Large Deviation Results for Dynamical Systems},
  author={Lai-Sang Young},
  year={2010}
}
We prove some large deviation estimates for continuous maps of compact metric spaces and apply them to attractors in differentiable dynamics, rate of escape problems, and to shift spaces. Introduction Consider a discrete time dynamical system generated by a self-map /: X O of some domain X. Let m be a reference measure on X, and let <p : X —► R be an observable. Suppose that £ J2"fx <p ° f converges to some constant lp m-a.e. This paper is concerned with the rate of convergence of this time… CONTINUE READING