Geodesic
Cohomology of dynamical systems
Izvestiya. Mathematics, Tome 6 (1972) no. 6, pp. 1278-1301 
A. N. Livshits. Cohomology of dynamical systems. Izvestiya. Mathematics, Tome 6 (1972) no. 6, pp. 1278-1301. http://geodesic.mathdoc.fr/item/IM2_1972_6_6_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper criteria for the cohomological nullity of functions on phase spaces of various dynamical systems (U-systems, topological Markov chains, Smale systems) with coefficients in certain groups are formulated and proved, and applications of these criteria are studied. (In the simplest case of a transformation $T\colon M\to M$, the cohomological nullity of a real function $f$ means that $f(x)=g(Tx)-g(x)$.)

[1] Livshits A. N., “Nekotorye svoistva gomologii U-sistem”, Matem. zametki, 10:5 (1971), 555–564 | Zbl

[2] Anosov D. V., “O kasatelnykh polyakh transversalnykh sloenii v U-sistemakh”, Matem. zametki, 2:5 (1967), 539–548 | MR | Zbl

[3] Teoriya algebr Li. Topologiya grupp Li, IIL, M., 1967

[4] Sinai Ya. G., “Markovskie razbieniya i U-diffeomorfizmy”, Funktsionalnyi analiz, 2:1 (1968), 64–89 | MR | Zbl

[5] Katok S. B., “Lineinye rasshireniya dinamicheskikh sistem i usloviya privodimosti”, Matem. zametki, 8:4 (1970), 451–463 | MR

[6] Smeil S., “Differentsiruemye dinamicheskie sistemy”, Uspekhi matem. nauk, XXV:1(151) (1970), 113–185 | MR

[7] Anosov D. V., Geodezicheskie potoki na zamknutykh rimanovykh mnogoobraziyakh otritsatelnoi krivizny, Tr. Mat. in-ta im. V. A. Steklova AN SSSR, 90, 1967 | MR

[8] Zigmund A., Trigonometricheskie ryady, Mir, M., 1965 | MR