Measures related to (e,n)-complexity functions

Details Measures related to (e,n)-complexity functions Measures related to (e,n)-complexity functions

2007-05-18

arxiv.org/abs/0705.2753v1

Mathematics

Dynamical Systems

Scientific paper

The (e,n)-complexity functions describe total instability of trajectories in dynamical systems. They reflect an ability of trajectories going through a Borel set to diverge on the distance $\epsilon$ during the time interval n. Behavior of the (e, n)-complexity functions as n goes to infinity is reflected in the properties of special measures. These measures are constructed as limits of atomic measures supported at points of (e,n)-separated sets. We study such measures. In particular, we prove that they are invariant if the (e,n)-complexity function grows subexponentially. Keywords: Topological entropy, complexity functions, separability.

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