Points with maximal Birkhoff average oscillation

Jinjun Li; Min Wu

Czechoslovak Mathematical Journal (2016)

  • Volume: 66, Issue: 1, page 223-241
  • ISSN: 0011-4642

Abstract

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Let f : X → 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.

How to cite

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Li, Jinjun, and Wu, Min. "Points with maximal Birkhoff average oscillation." Czechoslovak Mathematical Journal 66.1 (2016): 223-241. <http://eudml.org/doc/276808>.

@article{Li2016,
abstract = {Let $f\colon X\rightarrow X$ 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.},
author = {Li, Jinjun, Wu, Min},
journal = {Czechoslovak Mathematical Journal},
keywords = {irregular set; maximal Birkhoff average oscillation; specification property; residual set},
language = {eng},
number = {1},
pages = {223-241},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Points with maximal Birkhoff average oscillation},
url = {http://eudml.org/doc/276808},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Li, Jinjun
AU - Wu, Min
TI - Points with maximal Birkhoff average oscillation
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 1
SP - 223
EP - 241
AB - Let $f\colon X\rightarrow X$ 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.
LA - eng
KW - irregular set; maximal Birkhoff average oscillation; specification property; residual set
UR - http://eudml.org/doc/276808
ER -

References

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