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Background and Basics

  • Bruce P. Kitchens
Chapter
  • 756 Downloads
Part of the Universitext book series (UTX)

Abstract

We will be working with sequence spaces. There will be two types of sequence spaces. One is composed of one-sided infinite sequences and the other is composed of two-sided infinite sequences. These are metric spaces where two one-sided sequences are said to be close together if they agree for a long time at the beginning and two two-sided sequences are said to be close together if they agree for a long time around the center. In the first part of the book the sequences will have entries coming from a finite set and in the second part the entries will come from a countable set. When the entries are from a finite set the sequence space is usually homeomorphic to the standard Cantor set. The transformation we study will be the shift transformation which shifts each sequence once to the left. The richness of the dynamics does not arise from the topology of the space or the definition of the transformation but from the definition of which sequences belong to each space. We study subshifts of finite type. They are the sequence spaces characterized by having a finite rule which determines the sequences belonging to each space.

Keywords

Transition Matrix Zeta Function Periodic Point Finite Type Topological Entropy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Bruce P. Kitchens
    • 1
  1. 1.Mathematical Sciences DepartmentIBM T.J. Watson Research CenterYorktown HeightsUSA

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