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An introduction to ergodic theory - Walters P.

Walters P. An introduction to ergodic theory - London, 1982. - 251 p.
Download (direct link): anintroduction1982.djvu
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Reference:
245
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Index
а-limit set 123
Absolute continuity of measures 8 Affine transformation 21 conditions for ergodicity 31 conditions for minimality 122 conditions for mixing 50 conditions fur topological liansihvily 113 condition*. i-и unique rrgodii ity 162 entropy 102. 203 non- wandering set 126 topological entropy 203 Affinity of the entropy map 183 Algebra 3 Aperiodic
non-negative matrix 16 transformation 97 Automorphism of a torus 15 conditions for ergodicity 31 conditions for expansiveness 143 conditions for mixing 50 conditions for topological transitivity 132 entropy 102 topological entropy 203 Axiom A diffeomorphism 130, 226, 229
/3-shift 178
Banach-Stone theorem 136 Basis for a Hilbert space 10 Bernoulli
automorphism 106 shift 105 Hlikli<>/T\s crgodic theorem 34
Hlot к 5
Hoi cl tr algebra of a (opologieal space 10, IK, 146 Borel’s theorem on normal numbers
Centre of a continuous
transformation 126, 157 Character theory 12 Choquet’s theorem 153 Complete invariant 62, 103 Completely positive entropy 110 Conditional entropy 80, 84 expectation 9 Conjugacy
of measure-preserving transformations 59 of measure spaces 54 topological 133
248
Index
Continued fractions 24 Continuous spectrum 48 Countable basis for a measure space 10, 44
Countable Lebesgue spectrum 65 Countably additive 4
Density zero 43 Direct product of continuous transformations 174 of measure-preserving transformations 23, 99 of measure spaces 5 Discrete .spectrum
for measure-preserving transformations 64, 69 theorem 70 topological 135 Distal 130
Dominated convergence theorem 8 Doob’s martingale theorem 85
Eigenfunction of a continuous transformation 133 of a measure-preserving transformation 48, 68 Eigenvalue of a continuous transformation 133 of a measure-preserving transformation 48, 68 EndoninrphiMii of a compact group 20 coiuliiion* for ergodicity 30 conditions lor mixing 50 conditions for topological transitivity 132 entropy 102, 197 topological entropy 197 Endomorphism of a torus 15, 20 conditions for ergodicity 30, 31 conditions for mixing 50 conditions for topological transitivity 132 entropy 102, 203 topological entropy 203 Entropy conditional 80, 84 of an affine transformation 102, 203 of a Bernoulli shift 102 of a direct product 99 of an eigodic decomposition 186 of a Markov shift 103 of a measure-preserving transformation 87
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