Iterates of expanding maps

Moderate deviations for iterates of expanding maps

We provide a mild mixing condition that carries the C.L.T. for normalized empirical means of centered stationary sequence of bounded random variables to the whole range of moderate deviations. It is also key for the exponential convergence of the laws of empirical means. The motivating example for this work are iterates of expanding maps, equipped with their unique invariant measure.

Random Iterates of Monotone Maps

Lattice Isomorphisms and Iterates of Nonexpansive Maps

It is easy to see that the I, norm and the sup norm 11. Ilm (Ilxll, = max{Ix, I: 1 I i 5 n)) on I?’ are polyhedral. If E is a finite dimensional Banach space with a polyhedral norm 11. )I, D is a compact subset of E and f: D + D is a nonexpansive map, Weller [2] has shown that for each x E D, there again exists an integer px such that (1.1) holds. The original arguments did not give upper bound...

Equicontinuity of Iterates of Circle Maps Antonios

Let f be a continuous map of the circle to itsel Necessary and sufficient conditions are given for the family ofiterates {f"}= to be equicontinuous.

Iterates of semidifferentiable monotone homogeneous maps

We study the nonlinear eigenproblem for monotone additively homogeneous maps f : Rn → Rn, and more generally, for monotone multiplicatively homogeneous maps on cones. When f is convex, monotone and additively homogeneous, we describe the nonlinear eigenspace of f using its subdifferential (or its tangent affine maps) [AG03]. This yields in particular an uniqueness result for the eigenvector of ...