Ergodic theory of one dimensional Map

Ergodic theory for smooth one dimensional dynamical systems

In this paper we study measurable dynamics for the widest rea sonable class of smooth one dimensional maps Three principle de compositions are described in this class decomposition of the global measure theoretical attractor into primitive ones ergodic decompo sition and Hopf decomposition For maps with negative Schwarzian derivative this was done in the series of papers BL BL but the approach ...

Resonances for Large One-dimensional “ergodic” Systems

Abstract. The present paper is devoted to the study of resonances for one-dimensional quantum systems with a potential that is the restriction to some large box of an ergodic potential. For discrete models both on a half-line and on the whole line, we study the distributions of the resonances in the limit when the size of the box where the potential does not vanish goes to infinity. For periodi...

Ergodic Theory and Discrete One-dimensional Random Schr Odinger Operators: Uniform Existence of the Lyapunov Exponent

We review recent results which relate spectral theory of discrete one-dimensional Schrödinger operators over strictly ergodic systems to uniform existence of the Lyapunov exponent. In combination with suitable ergodic theorems this allows one to establish Cantor spectrum of Lebesgue measure zero for a large class of quasicrystal Schrödinger operators. The results can also be used to study non-u...

An introduction to Smooth Ergodic Theory for one-dimensional dynamical systems

Ergodic Properties of an Infinite One Dimensional Hard Rod System*

It is shown that an infinite one dimensional system of hard rods for which the "effective" velocities of the pulses (free velocity plus a drift term due to collisions) are bounded away from some neighborhood of 0 is Bernoulli. This generalizes a result of Sinai who showed that some hard rod systems are X-systems.