The consecutive numbering of the publications is determined by their chronological order. The aim of this preprint series is to make new research rapidly available for scientific discussion. Therefore, the responsibility for the contents is solely due to the authors. The publications will be distributed by the authors. Abstract For piecewise monotone… (More)
We extend a number of results from one dimensional dynamics based on spectral properties of the Ruelle-Perron-Frobenius transfer operator to Anosov diieomorphisms on compact manifolds. This allows to develop a direct operator approach to study ergodic properties of these maps. In particular, we show that it is possible to deene Banach spaces on which the… (More)
We study one-dimensional lattices of weakly coupled piecewise expanding interval maps as dynamical systems. Since neither the local maps need to have full branches nor the coupling map needs to be a homeomorphism of the infinite dimensional state space, we cannot use symbolic dynamics or other techniques from statistical mechanics. Instead we prove that the… (More)
We construct a mixing continuous piecewise linear map on [−1, 1] with the property that a two-dimensional lattice made of these maps with a linear north and east nearest neighbour coupling admits a phase transition. We also provide a modification of this construction where the local map is an expanding analytic circle map. The basic strategy is borroughed… (More)
We prove the existence of a unique SRB measure for a wide range of multidimensional weakly coupled map lattices. These include piecewise expanding maps with diffusive coupling.
In this note we give a computable criterion for a piecewise expanding interval map T to be mixing, which at the same time not only establishes explicit bounds on the spectral gap of the associated Perron Frobenius operator acting on the space of functions of bounded variation, but establishes strict contraction rates for this operator. Of course such a… (More)
– For piecewise expanding one-dimensional maps without periodic turning points we prove that isolated eigenvalues of small (random) perturbations of these maps are close to isolated eigenvalues of the unperturbed system. (Here " eigenvalue " means eigenvalue of the corresponding Perron-Frobenius operator acting on the space of functions of bounded variation… (More)
We prove a quenched central limit theorem for random walks with bounded increments in a randomly evolving environment on Z d. We assume that the transition probabilities of the walk depend not too strongly on the environment and that the evolution of the environment is Markovian with strong spatial and temporal mixing properties. 1. Introduction. The study… (More)
Let X R 2 be a nite union of bounded polytopes and let T : X ! X be piecewise aane and eventually expanding. Then the Perron-Probenius operator L of T is quasicompact as an operator on the space of functions of bounded variation on R 2 and its isolated eigenvalues (including multiplicities) are just the reciprocals of the poles of the dynamical zeta… (More)
We present a common framework to study decay and exchanges rates in a wide class of dynamical systems. Several applications, ranging form the metric theory of continuons fractions and the Shannon capacity of con-trained systems to the decay rate of metastable states, are given.