Measures related to (∈, n)-complexity functions
Complexity functions; Separability; Topological entropy
The (ε, 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 ε during the time interval n. Behavior of the (ε, 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 (ε, n)-separated sets. We study such measures. In particular, we prove that they are invariant if the (ε, n)-complexity function grows subexponentially.
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Discrete and Continuous Dynamical Systems
Generically Dependent Continuant
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