# Article

MSC: 37C45, 54E52, 54H20
Full entry | Fulltext not available (moving wall 24 months)
Keywords:
irregular set; maximal Birkhoff average oscillation; specification property; residual set
Summary:
Let $f\colon X\to X$ be a continuous map with the specification property on a compact metric space $X$. We introduce the notion of the maximal Birkhoff average oscillation, which is the worst'' divergence point for Birkhoff average. By constructing a kind of dynamical Moran subset, we prove that the set of points having maximal Birkhoff average oscillation is residual if it is not empty. As applications, we present the corresponding results for the Birkhoff averages for continuous functions on a repeller and locally maximal hyperbolic set.
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