On the speed of convergence to equilibrium statesfor multi-dimensional maps with indifferent periodic points

Abstract

We shall clarify the speed of L1-convergence of iterated transfer operators and rates of decay of correlationsfor multi-dimensional noninvertible maps with indifferent periodic points related to a class of functions which contains all piecewise Lipschitz functions. The essential issue for solving these problems is to clarify the speed of uniform convergence of transfer operators on compact sets excluding indifferent periodic points. Our results can be applicable to higher dimensionalcountable to one intermittent maps for which previous techniques on decay of correlations do not work.