Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
ALMOST ISOMORPHISM FOR COUNTABLE STATE MARKOV MIKE BOYLE, JEROME BUZZI, AND RICARDO GOMEZ
 

Summary: ALMOST ISOMORPHISM FOR COUNTABLE STATE MARKOV
SHIFTS
MIKE BOYLE, JEROME BUZZI, AND RICARDO GOMEZ
Dedicated to Peter Walters and Klaus Schmidt, on the occasion of their sixtieth birthdays.
Abstract. Countable state Markov shifts are a natural generalization of the
well-known subshifts of finite type. They are the subject of current research
both for their own sake and as models for smooth dynamical systems. In this
paper, we investigate their almost isomorphism and entropy conjugacy and ob-
tain a complete classification for the especially important class of strongly posi-
tive recurrent Markov shifts. This gives a complete classification up to entropy-
conjugacy of the natural extensions of smooth entropy-expanding maps, e.g.,
C smooth interval maps with non-zero topological entropy.
Contents
1. Introduction 1
2. Definitions and background 2
3. Magic words, almost isomorphism and entropy-conjugacy 5
4. Zeta functions 8
5. The Loops Lemma 10
6. Main Results 14
7. Application to other dynamical systems 16

  

Source: Aíza, Ricardo Gómez - Instituto de Matemáticas, Universidad Nacional Autónoma de México

 

Collections: Mathematics