Ergodic Theory on Compact Spaces |
Contents
| 1 | |
| 17 | |
6 | 24 |
7 | 32 |
Measures on the Shift Space | 41 |
Partitions and Generators | 49 |
Information and Entropy | 56 |
Computation of Entropy | 62 |
23 | 218 |
Basic Sets for Axiom | 224 |
Automorphisms of the Torus | 234 |
25 | 241 |
26 | 254 |
27 | 275 |
28 | 281 |
Ergodic Systems | 300 |
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Common terms and phrases
A₁ Anosov diffeomorphism atoms B₁ Bl(M Borel canonical coordinates compact construction Corollary defined Definition denote dense diam diffeomorphism disjoint eigenvalues ergodic measures ergodic theory exists expansive f.t. subshift F₁ finite type follows G₁ h-expansive hence homeomorphism htop(T implies integers invariant measures isomorphism J₁ K₁ Lebesgue lemma Let x,m,y lim sup M-blocks M-generator m.f.t.-subshift m.t. dynamical system M₁ Markov partition Math maximal entropy measure theoretic metric minimal n,c)-separated n₁ nonwandering set open cover open sets periodic points Proof Proposition R₁ resp Rohlin set satisfying sequence space specification property strictly ergodic subset subshift of finite system X,T t₁ theorem topological dynamical topological dynamical system topological entropy topologically mixing topologically transitive transformation uniquely ergodic V₁ X₁ y-invariant α α