Large deviation principles for non-uniformly hyperbolic rational maps
Large deviation principles for non-uniformly hyperbolic rational maps
Abstract We show some level-2 large deviation principles for rational maps satisfying a strong form of non-uniform hyperbolicity, called āTopological ColletāEckmannā. More precisely, we prove a large deviation principle for the distribution of iterated preimages, periodic points, and Birkhoff averages. For this purpose we show that each Hƶlder continuous potential ā¦