Contents
Preface ix
Part A.
Resolving Markov Chains onto Bernoulli Shifts 1
1. Introduction 3
2. Weighted graphs and polynomial matrices 6
3. The main results 11
4. Markov chains and regular isomorphism 18
5. Necessity of the conditions 25
6. Totally conforming eigenvectors and the one-variable case 31
7. Splitting the conforming eigenvector in the one-variable case 40
8. Totally conforming eigenvectors for the general case 53
9. Splitting the conforming eigenvector in the general case 58
Bibliography 72
Part B.
On Large Powers of Positive Polynomials in Several Variables 75
1. Introduction 77
2. Structure of Log(pn) 80
3. Entropy and equilibrium distributions for w G W(p) 85
4. Equilibrium distributions and coefficients of p n 90
5. Proofs of the estimates 93
Bibliography 98
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