Points with maximal Birkhoff average oscillation

Li, Jinjun ; Wu, Min

Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 223-241

Abstract (VO)

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.

Détail

DOI : 10.1007/s10587-016-0252-3

Classification : 37C45, 54E52, 54H20
Keywords: irregular set; maximal Birkhoff average oscillation; specification property; residual set

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