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January & February  2008, 22(1&2): 23-34. doi: 10.3934/dcds.2008.22.23

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

Valentin Afraimovich 1, and  Lev Glebsky 1,

1. 

IICO-UASLP, Karakorum 1470, Lomas 4a, 78210, San Luis Potosi, S.L.P., Mexico, Mexico

Received  May 2007 Revised  September 2007 Published  June 2008

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.
Keywords: separability., Topological entropy, complexity functions.
Mathematics Subject Classification: 28C15, 37C9.
Citation: Valentin Afraimovich, Lev Glebsky. Measures related to $(\epsilon,n)$-complexity functions. Discrete & Continuous Dynamical Systems - A, 2008, 22 (1&2) : 23-34. doi: 10.3934/dcds.2008.22.23
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