… In this case we call the (one or two-sided) measure-preserving system the Markov shift
determined by p and P. Points in the space are conveniently pictured as infinite paths in a …

… to measure the complexity of entropy zero dynamical systems. For measure preserving systems,
… a new insight for analyzing entropy zero systems. We also define the dimension set of a …

… ) we arrive at a space with a bounded measure and a measure preserving transformation.
After normalizing we obtain a probability measure preserving rank-one system (X,B, µ, T). …

… is equivalent to building our system on the unit interval by … measurepreserving system
we mean a nonatomic Lebesgue probability space together with an invertible measure-preserving …

… an ergodic invertible measure preserving transformation on … of positive measure, the class
of measure preserving T with a … an ergodic invertible measure preserving transformation T and …

… with dynamical systems preserving an infinite measure that … for dynamical systems with infinite
measure. Invent. Math. … associated with dynamical systems with infinite measure. Moreover…

… that the invariant measure of open volume-preserving systems may become singular if …
deterministic diffusion in strictly volume-preserving systems of large spatial extension such …

… system of 2n differential equations induces in the phase space of the system a measure-preserving …
invariant the 2n-dimensional measure. Making use of one or more integrals of the …

… , it differs by a factor from a measure preserving system and is the basis for higher dimensional
measure preserving systems. We insist that the three systems be observable. In the first …

… measurepreserving mappings. A most pictorial example is the behavior of magnetic field lines
in a toroidal system. A … lines of force around the system from one intersection with the cross …