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Measures related to $(\epsilon,n)$-complexity functions

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  • The $(\epsilon,n)$-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 $(\epsilon, n)$-complexity functions as $n\to\infty$ is reflected in the properties of special measures. These measures are constructed as limits of atomic measures supported at points of $(\epsilon,n)$-separated sets. We study such measures. In particular, we prove that they are invariant if the $(\epsilon,n)$-complexity function grows subexponentially.
    Mathematics Subject Classification: 28C15, 37C99.


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