Advertisement

Symbolic Dynamics

  • Luís BarreiraEmail author
  • Claudia Valls
Chapter
Part of the Problem Books in Mathematics book series (PBM)

Abstract

Show that for each \(\omega \in \Sigma _k^+\) and \(r>0\) the open ball
$$ B_{d_\beta }(\omega , r)=\bigl \{\omega '\in \Sigma _k^+:d_\beta (\omega ',\omega )<r\bigr \} $$
is a cylinder, that is, there exist integers \(i_1,\ldots , i_n \in \{1,\ldots , k\}\) with \(n=n(r)\) such that
$$ B_{d_\beta } (\omega , r)=C_{i_1 \cdots i_n}:=\bigl \{\omega \in \Sigma _k^+ : i_j(\omega )=i_j \ \text {for j=1,\ldots , n}\bigr \}. $$

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal
  2. 2.Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal

Personalised recommendations