iv CONTENT S
9.3. Cohomologica l equation s fo r measure-preservin g transformation s
and flow s 5 9
10. Structur e o f equivalence classe s 6 2
10.1. Majorizatio n an d densit y i n L
1
6 2
10.2. Continuou s an d almos t differentiabl e representation s 6 6
11. Rigidit y an d stabilit y 6 8
11.1. Definition s 6 8
11.2. Translation s o f the toru s an d smoot h rigidit y 7 0
11.3. Stabilit y o f Holder cocycle s for transformation s wit h specificatio n 7 4
11.4. Livshit z theor y 7 8
11.5. Invarian t distribution s an d stability of partially hyperbolic systems 8 1
11.6. Stabilit y determined by invariant distributions in parabolic systems 8 5
12. Wil d cochain s wit h tam e coboundarie s 8 9
12.1. Continuou s cocycle s ove r measure-preservin g homeomorphism s 9 0
12.2. Fas t approximatio n an d C°° cocycle s 9 4
12.3. Minima l nonergodi c diffeomorphism s o f T 2 9 7
12.4. Minima l nonergodi c interva l exchang e transformation s 9 8
13. Non-trivia l cocycle s 102
13.1. Tw o genera l criteri a 102
13.2. Th e cas e of fast C°° approximatio n 105
13.3. Weakl y mixin g flow s o n T 2 107
13.4. Ergodicit y o f analyti c cylindrica l cascade s 112
13.5. Wea k mixin g o f specia l flow s ove r interva l exchang e transforma -
tions 14
References 117
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