arXiv:1709.06327 Abstract | arXiv Analytics

arXiv:1709.06327 [math.DS]Abstract References Reviews Resources

Ergodic averaging with and without invariant measures

Published 2017-09-19Version 1

The classical Birkhoff ergodic theorem in its most popular version says that the time average along a single typical trajectory of a dynamical system is equal to the space average with respect to the ergodic invariant distribution. This result is one of the cornerstones of the entire ergodic theory and its numerous applications. Two questions related to this subject will be addressed: how large is the set of typical trajectories, in particular in the case when there are no invariant distributions, and how the answer is connected to properties of the so called natural measures (limits of images of "good" measures under the action of the system).

Comments: 17 pages, 1 figure

Categories: math.DS

Subjects: 28D05, 37A30

Keywords: invariant measures, ergodic averaging, entire ergodic theory, classical birkhoff ergodic theorem, ergodic invariant distribution

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