Measures related to (ǫ, n)-complexity functions
نویسندگان
چکیده
The (ǫ, 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 ǫ during the time interval n. Behavior of the (ǫ, n)-complexity functions as n → ∞ is reflected in the properties of special measures. These measures are constructed as limits of atomic measures supported at points of (ǫ, n)-separated sets. We study such measures. In particular, we prove that they are invariant if the (ǫ, n)-complexity function grows subexponentially. keywords Topological entropy, complexity functions, separability. AMC: 28C15, 37C99
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