On the relations among various entropy characteristics of dynamical systems
Izvestiya. Mathematics , Tome 5 (1971) no. 2, pp. 337-378.

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This paper deals with the relation between topological entropy and $\varepsilon$-entropy of the space of segments of trajectories of dynamical systems, as well as the relation between topological and metrical entropies. The results obtained are applied to some classical dynamical systems.
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E. I. Dinaburg. On the relations among various entropy characteristics of dynamical systems. Izvestiya. Mathematics , Tome 5 (1971) no. 2, pp. 337-378. http://geodesic.mathdoc.fr/item/IM2_1971_5_2_a4/

[1] Adler R. L., Konheim A. G., McAndrew M. H., “Topological entropy”, Trans. Amer. Math. Soc., 114:2 (1965), 309–319 | DOI | MR | Zbl

[2] Aleksandpov P. S., Kombinatornaya topologiya, OGIZ, M., 1947 | MR

[3] Alekseev V. M., “Kvazisluchainye dinamicheskie sistemy. I. Kvazisluchainye diffeomorfizmy”, Matem. sb., 76(118) (1968), 72–134 | Zbl

[4] Anosov D. V., Sinai Ya. G., “Nekotorye gladkie ergodicheskie sistemy”, Uspekhi matem. nauk, 22:5 (1967), 107–172 | MR | Zbl

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

[6] Billingsley P., Convergense of Probability Measures, Wiley, New York, 1968 | MR | Zbl

[7] Bowen R., Topological Entropy and Axiom A, preprint, Warwick, Coventry, 1969 | MR

[8] Bowen R., Periodic Points and Axiom A*, preprint, Warwick, Coventry, 1969 | MR

[9] Gurevich B. M., “Topologicheskaya entropiya schetnoi tsepi Markova”, Dokl. AN SSSR, 187:4 (1969), 715–718 | Zbl

[10] Gurevich V., Volmen G., Teoriya razmernosti, IL, M., 1948

[11] Dei M. M., Normirovannye lineinye prostranstva, IL, M., 1961

[12] Kolmogorov A. N., “Novyi metricheskii invariant tranzitivnykh dinamicheskikh sistem i avtomorfizmov prostranstv Lebega”, Dokl. AN SSSR, 119:5 (1958), 861–864 | MR | Zbl

[13] Kolmogorov A. N., “Ob entropii na edinitsu vremeni, kak metricheskom invariante avtomorfizmov”, Dokl. AN SSSR, 124:4 (1959), 754–755 | MR | Zbl

[14] Kolmogorov A. N., Tikhomirov V. M., “$\varepsilon$-entropiya i $\varepsilon$-emkost mnozhestv v funktsionalnykh prostranstvakh”, Uspekhi matem. nauk, 14:2 (1959), 3–86 | MR

[15] Conze J. P., “Points periodique et entropie topologique”, Comp. rend. Acad. Sci., 267:3 (1968), 149–152 | MR | Zbl

[16] Kupatovskii K., Topologiya, t. I, Mir, M., 1969

[17] Kryzewski K., “Note on topological entropy”, Bull. Acad. polon. Sci., XVI:6 (1968), 465–467 | MR

[18] Margulis G. A., Nekotorye voprosy teorii $Y$-sistem, Dissertatsiya, MGU, 1970

[19] Milnor Dzh., Teoriya Morsa, Mir, M., 1965 | MR

[20] Nemytskii V. V., Stepanov V. V., Kachestvennaya teoriya differentsialnykh uravnenii, Gostekhizdat, M., L., 1949

[21] Parry W., “Intrinsic Markov chains”, Trans. Amer. Math. Soc., 114:2 (1965), 55–66 | MR

[22] Parry W., “Symbolic dinamics and transformations of the unit interval”, Trans. Amer. Math. Soc., 122:2 (1966), 368–378 | DOI | MR | Zbl

[23] Pitskel B. S., “Soglasovannaya s topologiei metrika, invariantnaya otnositelno zadannogo gomeomorfizma prostranstva posledovatelnostei i svoistva topologicheskikh invariantov tipa entropii”, Uspekhi matem. nauk, 24:5 (1969), 222–223

[24] Rotenberg A. R., “Nekotorye svoistva topologicheskikh tsepei Markova i topologicheskie invarianty tipa entropii”, Uspekhi matem. nauk, 24:4 (1969), 186–187

[25] Rokhlin V. A., “Ob osnovnykh ponyatiyakh teorii mery”, Matem. sb., 67:1 (1949), 107–150 | Zbl

[26] Rokhlin V. A., “Novyi progress v teorii preobrazovanii s invariantnoi meroi”, Uspekhi matem. nauk, 15:4 (1960), 3–26 | MR | Zbl

[27] Rokhlin V. A., “Lektsii po entropiinoi teorii preobrazovanii s invariantnoi meroi”, Uspekhi matem. nauk, 22:5 (1967), 3–56 | Zbl

[28] Sinai Ya. G., “O ponyatii entropii dinamicheskoi sistemy”, Dokl. AN SSSR, 124:4 (1959), 768–771 | MR | Zbl

[29] Sinai Ya. G., “K obosnovaniyu ergodicheskoi gipotezy dlya odnoi dinamicheskoi sistemy statisticheskoi mekhaniki”, Dokl. AN SSSR, 153:6 (1963), 1261–1264 | MR

[30] Sinai Ya. G., Klassicheskie dinamicheskie sistemy so schetnokratnym lebegovskim spektrom. Slabyi izomorfizm dinamicheskikh sistem, Dissertatsiya, MGU, 1964

[31] Sinai Ya. G., “Klassicheskie dinamicheskie sistemy so schetnokratnym lebegovskim spektrom. II”, Izv. AN SSSR. Ser. matem., 30:1 (1966), 15–68 | MR | Zbl

[32] Sinai Ya. G., “Asimptotika chisla zamknutykh geodezicheskikh na kompaktnykh mnogoobraziyakh otritsatelnoi krivizny”, Izv. AN SSSR. Ser. matem., 30:6 (1966), 1275–1296 | MR | Zbl

[33] Smale S., “Diffeomorphisms with many periodic points”, Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), Princeton Univ. Press, Princeton, N.J., 1965, 63–80 | MR | Zbl

[34] Smale S., “Differentiable dynamical sistems”, Bull. Amer. Math. Soc., 73:6 (1967), 747–817 | DOI | MR

[35] Shilnikov L. P., “Ob odnoi zadache Puankare–Birkgofa”, Matem. sb., 74 (1967), 378–397

[36] Dinaburg E. I., “Odin primer vychisleniya topologicheskoi entropii”, Uspekhi matem. nauk, 23:4 (1968), 249–250 | MR | Zbl

[37] Dinaburg E. I., “Sootnoshenie mezhdu topologicheskoi entropiei i metricheskoi entropiei”, Dokl. AN SSSR, 190:1 (1970), 19–22 | MR | Zbl