[Aar97] J., Aaronson. An introduction to infinite ergodic theory, volume 50 of Mathematical Surveys and Monographs. American Mathematical Society, 1997.
[AB] A., Avila and J., Bochi. Proof of the subadditive ergodic theorem. Preprint www.mat.puc-rio.br/~jairo/docs/kingbirk.pdf.
[AF07] A., Avila and G., Forni. Weak mixing for interval exchange transformations and translation flows. Ann. Math., 165:637–664, 2007.
[AKM65] R., Adler, A., Konheim and M., McAndrew. Topological entropy. Trans. Amer. Math. Soc., 114:309–319, 1965.
[AKN06] V., Arnold, V., Kozlov and A., Neishtadt. Mathematical aspects of classical and celestial mechanics, volume 3 of Encyclopaedia of Mathematical Sciences. Springer-Verlag, third edition, 2006. [Dynamical systems. III], Translated from the Russian original by E., Khukhro.
[Ano67] D. V., Anosov. Geodesic flows on closed Riemannian manifolds of negative curvature. Proc. Steklov Math. Inst., 90:1–235, 1967.
[Arn78] V. I., Arnold. Mathematical methods of classical mechanics. Springer-Verlag, 1978.
[AS67] D. V., Anosov and Ya. G., Sinai. Certain smooth ergodic systems. Russian Math. Surveys, 22:103–167, 1967.
[Bal00] V., Baladi. Positive transfer operators and decay of correlations. World Scientific Publishing Co. Inc., 2000.
[BDV05] C., Bonatti, L. J., Díaz and M., Viana. Dynamics beyond uniform hyperbolicity, volume 102 of Encyclopaedia of Mathematical Sciences. Springer-Verlag, 2005.
[Bil68] P., Billingsley. Convergence of probability measures. John Wiley & Sons Inc., 1968.
[Bil71] P., Billingsley. Weak convergence of measures: Applications in probability. Society for Industrial and Applied Mathematics, 1971. Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 5.
[Bir13] G. D., Birkhoff. Proof of Poincaré's last Geometric Theorem. Trans. Amer. Math. Soc., 14:14–22, 1913.
[Bir67] G., Birkhoff. Lattice theory, volume 25. A.M.S. Colloq. Publ., 1967.
[BK83] M., Brin and A., Katok. On local entropy. In Geometric dynamics (Rio de Janeiro, 1981), volume 1007 of Lecture Notes in Math., pages 30–38. Springer-Verlag, 1983.
[BLY] D., Burguet, G., Liao and J., Yang. Asymptotic h-expansiveness rate of C8 maps. arxiv:1404.1771.
[Bos86] J.-B., Bost. Tores invariants des syst`emes hamiltoniens. Astérisque, 133–134:113–157, 1986.
[Bos93] M., Boshernitzan. Quantitative recurrence results. Invent. Math., 113(3): 617–631, 1993.
[Bow71] R., Bowen. Entropy for group endomorphisms and homogeneous spaces. Trans. Amer. Math. Soc., 153:401–414, 1971.
[Bow72] R., Bowen. Entropy expansive maps. Trans. Am. Math. Soc., 164:323–331, 1972.
[Bow75a] R., Bowen. Equilibrium states and the ergodic theory of Anosov diffeomorphisms, volume 470 of Lect. Notes in Math. Springer-Verlag, 1975.
[Bow75b] R., Bowen. A horseshoe with positive measure. Invent. Math., 29:203–204, 1975.
[Bow78] R., Bowen. Entropy and the fundamental group. In The Structure of Attractors in Dynamical Systems, volume 668 of Lecture Notes in Math., pages 21–29. Springer-Verlag, 1978.
[BS00] L., Barreira and J., Schmeling. Sets of “non-typical” points have full topological entropy and full Hausdorff dimension. Israel J. Math., 116:29–70, 2000.
[Buz97] J., Buzzi. Intrinsic ergodicity for smooth interval maps. Israel J. Math, 100:125–161, 1997.
[Car70] H., Cartan. Differential forms. Hermann, 1970.
[Cas04] A. A., Castro. Teoria da medida. Projeto Euclides. IMPA, 2004.
[Cla72] J., Clark. A Kolmogorov shift with no roots. ProQuest LLC, Ann Arbor, MI, 1972. PhD. Thesis, Stanford University.
[dC79] M. do, Carmo. Geometria riemanniana, volume 10 of Projeto Euclides. Instituto de Matemática Pura e Aplicada, 1979.
[Dei85] K., Deimling. Nonlinear functional analysis. Springer-Verlag, 1985.
[Din70] E., Dinaburg. A correlation between topological entropy and metric entropy. Dokl. Akad. Nauk SSSR, 190:19–22, 1970.
[Din71] E., Dinaburg. A connection between various entropy characterizations of dynamical systems. Izv. Akad. Nauk SSSR Ser. Mat., 35:324–366, 1971.
[dlL93] R. de la, Llave. Introduction to K.A.M. theory. In Computational physics (Almuñécar, 1992), pages 73–105. World Sci. Publ., 1993.
[DS57] N., Dunford and J., Schwarz. Linear operators I: General theory.Wiley & Sons, 1957.
[DS63] N., Dunford and J., Schwarz. Linear operators II: Spectral theory. Wiley & Sons, 1963.
[Dug66] J., Dugundji. Topology. Allyn and Bacon Inc., 1966.
[Edw79] R. E., Edwards. Fourier series. A modern introduction. Vol. 1, volume 64 of Graduate Texts in Mathematics. Springer-Verlag, second edition, 1979.
[ET36] P., Erdös and P., Turán. On some sequences of integers. J. London. Math. Soc., 11:261–264, 1936.
[Fal90] K., Falconer. Fractal geometry: Mathematical foundations and applications. John Wiley & Sons Ltd., 1990.
[Fer02] R., Fernandez. Medida e integraç ão. Projeto Euclides. IMPA, 2002.
[FFT09] S., Ferenczi, A., Fisher and M., Talet. Minimality and unique ergodicity for adic transformations. J. Anal. Math., 109:1–31, 2009.
[FO70] N., Friedman and D., Ornstein. On isomorphism of weak Bernoulli transformations. Advances in Math., 5:365–394, 1970.
[Fri69] N., Friedman. Introduction to ergodic theory. Van Nostrand, 1969.
[Fur61] H., Furstenberg. Strict ergodicity and transformation of the torus. Amer. J. Math., 83:573–601, 1961.
[Fur77] H., Furstenberg. Ergodic behavior and a theorem of Szemerédi on arithmetic progressions. J. d'Analyse Math., 31:204–256, 1977.
[Fur81] H., Furstenberg. Recurrence in ergodic theory and combinatorial number theory. Princeton University Press, 1981.
[Goo71a] T., Goodman. Relating topological entropy and measure entropy. Bull. London Math. Soc., 3:176–180, 1971.
[Goo71b] G., Goodwin. Optimal input signals for nonlinear-system identification. Proc. Inst. Elec. Engrs., 118:922–926, 1971.
[GT08] B., Green and T., Tao. The primes contain arbitrarily long arithmetic progressions. Ann. of Math., 167:481–547, 2008.
[Gur61] B. M., Gurevič. The entropy of horocycle flows. Dokl. Akad. Nauk SSSR, 136:768–770, 1961.
[Hal50] P., Halmos. Measure Theory. Van Nostrand, 1950.
[Hal51] P., Halmos. Introduction to Hilbert space and the theory of spectral multiplicity. Chelsea Publishing Company, 1951.
[Hay] N., Haydn. Multiple measures of maximal entropy and equilibrium states for one-dimensional subshifts. Preprint, Penn State University.
[Hir94] M., Hirsch. Differential topology, volume 33 of Graduate Texts in Mathematics. Springer-Verlag, 1994. Corrected reprint of the 1976 original.
[Hof77] F., Hofbauer. Examples for the nonuniqueness of the equilibrium state. Trans. Amer. Math. Soc., 228:223–241, 1977.
[Hop39] E. F., Hopf. Statistik der geodätischen Linien in Mannigfaltigkeiten negativer Krümmung. Ber. Verh. Sächs. Akad. Wiss. Leipzig, 91:261–304, 1939.
[HvN42] P., Halmos and J. von, Neumann. Operator methods in classical mechanics. II. Ann. Math., 43:332–350, 1942.
[Jac60] K., Jacobs. Neuere Methoden und Ergebnisse der Ergodentheorie. Ergebnisse der Mathematik und ihrer Grenzgebiete. N. F., Heft 29. Springer-Verlag, 1960.
[Jac63] K., Jacobs. Lecture notes on ergodic theory, 1962/63. Parts I, II. Matematisk Institut, Aarhus Universitet, Aarhus, 1963.
[Kal82] S., Kalikow. T, T-1 transformation is not loosely Bernoulli. Ann. Math., 115:393–409, 1982.
[Kat71] Yi., Katznelson. Ergodic automorphisms of Tn are Bernoulli shifts. Israel J. Math., 10:186–195, 1971.
[Kat80] A., Katok. Lyapunov exponents, entropy and periodic points of diffeomorphisms. Publ. Math. IHES, 51:137–173, 1980.
[Kea75] M., Keane. Interval exchange transformations. Math. Zeit., 141:25–31, 1975.
[KM10] S., Kalikow and R., McCutcheon. An outline of ergodic theory, volume 122 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, 2010.
[Kok35] J. F., Koksma. Ein mengentheoretischer Satz über die Gleichverteilung modulo Eins. Compositio Math., 2:250–258, 1935.
[KR80] M., Keane and G., Rauzy. Stricte ergodicité des échanges d'intervalles. Math. Zeit., 174:203–212, 1980.
[Kri70] W., Krieger. On entropy and generators of measure-preserving transformations. Trans. Amer. Math. Soc., 149:453–464, 1970.
[Kri75] W., Krieger. On the uniqueness of the equilibrium state. Math. Systems Theory, 8:97–104, 1974/75.
[KSS91] A., Krámli, N., Simányi and D., Szász. The K-property of three billiard balls. Ann. Math., 133:37–72, 1991.
[KSS92] A., Krámli, N., Simányi and D., Szász. The K-property of four billiard balls. Comm. Math. Phys., 144:107–148, 1992.
[KW82] Y., Katznelson and B., Weiss. A simple proof of some ergodic theorems. Israel J. Math., 42:291–296, 1982.
[Lan73] O., Lanford. Entropy and equilibrium states in classical statistical mechanics. In Statistical mechanics and mathematical problems, volume 20 of Lecture Notes in Physics, page 1–113. Springer-Verlag, 1973.
[Led84] F., Ledrappier. Propriétés ergodiques des mesures de Sinaï. Publ. Math. I.H.E.S., 59:163–188, 1984.
[Lin77] D., Lind. The structure of skew products with ergodic group actions. Israel J. Math., 28:205–248, 1977.
[LS82] F., Ledrappier and J.-M., Strelcyn. A proof of the estimation from below in Pesin's entropy formula. Ergod. Th & Dynam. Sys, 2:203–219, 1982.
[LVY13] G., Liao, M., Viana and J., Yang. The entropy conjecture for diffeomorphisms away from tangencies. J. Eur. Math. Soc. (JEMS), 15(6):2043–2060, 2013.
[LY85a] F., Ledrappier and L.-S., Young. The metric entropy of diffeomorphisms. I. Characterization of measures satisfying Pesin's entropy formula. Ann. Math., 122:509–539, 1985.
[LY85b] F., Ledrappier and L.-S., Young. The metric entropy of diffeomorphisms. II. Relations between entropy, exponents and dimension. Ann. Math., 122:540–574, 1985.
[Man75] A., Manning. Topological entropy and the first homology group. In Dynamical Systems, Warwick, 1974, volume 468 of Lecture Notes in Math., pages 185–190. Springer-Verlag, 1975.
[Mañ85] R., Mañé. Hyperbolicity, sinks and measure in one-dimensional dynamics. Comm. Math. Phys., 100:495–524, 1985.
[Mañ87] R., Mañé. Ergodic theory and differentiable dynamics. Springer-Verlag, 1987.
[Mas82] H., Masur. Interval exchange transformations and measured foliations. Ann. Math, 115:169–200, 1982.
[Mey00] C., Meyer. Matrix analysis and applied linear algebra. Society for Industrial and Applied Mathematics (SIAM), 2000.
[Mis73] M., Misiurewicz. Diffeomorphim without any measure of maximal entropy. Bull. Acad. Pol. Sci., 21:903–910, 1973.
[Mis76] M., Misiurewicz. A short proof of the variational principle for a Z+N action on a compact space. Asterisque, 40:147–187, 1976.
[MP77a] M., Misiurewicz and F., Przytycki. Entropy conjecture for tori. Bull. Pol. Acad. Sci. Math., 25:575–578, 1977.
[MP77b] M., Misiurewicz and F., Przytycki. Topological entropy and degree of smooth mappings. Bull. Pol. Acad. Sci. Math., 25:573–574, 1977.
[MP08] W., Marzantowicz and F., Przytycki. Estimates of the topological entropy from below for continuous self-maps on some compact manifolds. Discrete Contin. Dyn. Syst. Ser., 21:501–512, 2008.
[MT78] G., Miles and R., Thomas. Generalized torus automorphisms are Bernoullian. Advances in Math. Supplementary Studies, 2:231–249, 1978.
[New88] S., Newhouse. Entropy and volume. Ergodic Theory Dynam. Systems, 8*(Charles Conley Memorial Issue):283–299, 1988.
[New90] S., Newhouse. Continuity properties of entropy. Ann. Math., 129:215–235, 1990. Errata in Ann. Math. 131:409–410, 1990.
[NP66] D., Newton and W., Parry. On a factor automorphism of a normal dynamical system. Ann. Math. Statist., 37:1528–1533, 1966.
[NR97] A., Nogueira and D., Rudolph. Topological weak-mixing of interval exchange maps. Ergod. Th. & Dynam. Sys., 17:1183–1209, 1997.
[Orn60] D., Ornstein. On invariant measures. Bull. Amer. Math. Soc., 66:297–300, 1960.
[Orn70] D., Ornstein. Bernoulli shifts with the same entropy are isomorphic. Advances in Math., 4:337–352 (1970), 1970.
[Orn72] Donald S., Ornstein. On the root problem in ergodic theory. In Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. II: Probability theory, pages 347–356. Univ. California Press, 1972.
[Orn74] D., Ornstein. Ergodic theory, randomness, and dynamical systems. Yale University Press, 1974. James K. Whittemore Lectures in Mathematics given at Yale University, Yale Mathematical Monographs, No. 5.
[OS73] D., Ornstein and P., Shields. An uncountable family of K-automorphisms. Advances in Math., 10:63–88, 1973.
[OU41] J. C., Oxtoby and S. M., Ulam. Measure-preserving homeomorphisms and metrical transitivity. Ann. Math., 42:874–920, 1941.
[Par53] O. S., Parasyuk. Flows of horocycles on surfaces of constant negative curvature. Uspehi Matem. Nauk (N.S.), 8:125–126, 1953.
[Pes77] Ya. B., Pesin. Characteristic Lyapunov exponents and smooth ergodic theory. Russian Math. Surveys, 324:55–114, 1977.
[Pes97] Ya., Pesin. Dimension theory in dynamical systems: Contemporary views and applications. University of Chicago Press, 1997.
[Pet83] K., Petersen. Ergodic theory. Cambridge University Press, 1983.
[Phe93] R., Phelps. Convex functions, monotone operators and differentiability, volume 1364 of Lecture Notes in Mathematics. Springer-Verlag, second edition, 1993.
[Pin60] M. S., Pinsker. Informatsiya i informatsionnaya ustoichivostsluchainykh velichin i protsessov. Problemy Peredači Informacii, Vyp. 7. Izdat. Akad. Nauk SSSR, 1960.
[PT93] J., Palis and F., Takens. Hyperbolicity and sensitive-chaotic dynamics at homoclinic bifurcations. Cambridge University Press, 1993.
[PU10] F., Przytycki and M., Urbański. Conformal fractals: Ergodic theory methods, volume 371 of London Mathematical Society Lecture Note Series. Cambridge University Press, 2010.
[PW72a] W., Parry and P., Walters. Errata: “Endomorphisms of a Lebesgue space”. Bull. Amer. Math. Soc., 78:628, 1972.
[PW72b] W., Parry and P., Walters. Endomorphisms of a Lebesgue space. Bull. Amer. Math. Soc., 78:272–276, 1972.
[PY98] M., Pollicott and M., Yuri. Dynamical systems and ergodic theory, volume 40 of London Mathematical Society Student Texts. Cambridge University Press, 1998.
[Qua99] A., Quas. Most expanding maps have no absolutely continuous invariant mesure. Studia Math., 134:69–78, 1999.
[Que87] M., Queffélec. Substitution dynamical systems—spectral analysis, volume 1294 of Lecture Notes in Mathematics. Springer-Verlag, 1987.
[Rok61] V. A., Rokhlin. Exact endomorphisms of a Lebesgue space. Izv. Akad. Nauk SSSR Ser. Mat., 25:499–530, 1961.
[Rok62] V. A., Rokhlin. On the fundamental ideas of measure theory. A. M. S. Transl., 10:1–54, 1962. Transl. from Mat. Sbornik 25 (1949), 107–150. First published by the A. M. S. in 1952 as Translation Number 71.
[Rok67a] V. A., Rokhlin. Lectures on the entropy theory of measure-preserving transformations. Russ. Math. Surv., 22(5):1–52, 1967. Transl. from Uspekhi Mat. Nauk. 22(5) (1967), 3–56.
[Rok67b] V. A., Rokhlin. Metric properties of endomorphisms of compact commutative groups. Amer. Math. Soc. Transl., 64:244–252, 1967.
[Roy63] H. L., Royden. Real analysis. Macmillan, 1963.
[RS61] V. A., Rokhlin and Ja. G., Sinaĭ. The structure and properties of invariant measurable partitions. Dokl. Akad. Nauk SSSR, 141:1038–1041, 1961.
[Rud87] W., Rudin. Real and complex analysis. McGraw-Hill, 1987.
[Rue73] D., Ruelle. Statistical mechanics on a compact set with Z? action satisfying expansiveness and specification. Trans. Amer. Math. Soc., 186:237–251, 1973.
[Rue78] D., Ruelle. An inequality for the entropy of differentiable maps. Bull. Braz. Math. Soc., 9:83–87, 1978.
[Rue04] D., Ruelle. Thermodynamic formalism: The mathematical structures of equilibrium statistical mechanics. Cambridge Mathematical Library. Cambridge University Press, second edition, 2004.
[RY80] C., Robinson and L. S., Young. Nonabsolutely continuous foliations for an Anosov diffeomorphism. Invent. Math., 61:159–176, 1980.
[SC87] Ya., Sinaĭ and Nikolay, Chernov. Ergodic properties of some systems of two-dimensional disks and three-dimensional balls. Uspekhi Mat. Nauk, 42:153–174, 256, 1987.
[Shu69] M., Shub. Endomorphisms of compact differentiable manifolds. Amer. Journal of Math., 91:129–155, 1969.
[Shu74] M., Shub. Dynamical systems, filtrations and entropy. Bull. Amer. Math. Soc., 80:27–41, 1974.
[Sim02] N., Simányi. The complete hyperbolicity of cylindric billiards. Ergodic Theory Dynam. Systems, 22:281–302, 2002.
[Sin63] Ya., Sinaĭ. On the foundations of the ergodic hypothesis for a dynamical system of statistical mechanics. Soviet. Math. Dokl., 4:1818–1822, 1963.
[Sin70] Ya., Sinaĭ. Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards. Uspehi Mat. Nauk, 25:141–192, 1970.
[Ste58] E., Sternberg. On the structure of local homeomorphisms of Euclidean n-space – II. Amer. J. Math., 80:623–631, 1958.
[SW75] M., Shub and R., Williams. Entropy and stability. Topology, 14:329–338, 1975.
[SX10] R., Saghin and Z., Xia. The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center. Topology Appl., 157:29–34, 2010.
[Sze75] S., Szemerédi. On sets of integers containing no k elements in arithmetic progression. Acta Arith., 27:199–245, 1975.
[vdW27] B. van der, Waerden. Beweis eibe Baudetschen Vermutung. Nieuw Arch. Wisk., 15:212–216, 1927.
[Vee82] W., Veech. Gauss measures for transformations on the space of interval exchange maps. Ann. of Math., 115:201–242, 1982.
[Ver99] Alberto, Verjovsky. Sistemas de Anosov, volume 9 of Monographs of the Institute of Mathematics and Related Sciences. Instituto de Matemática y Ciencias Afines, IMCA, Lima, 1999.
[Via14] M., Viana. Lectures on Lyapunov exponents. Cambridge University Press, 2014.
[VO14] M., Viana and K., Oliveira. Fundamentos da Teoria Ergódica. Coleç ão Fronteiras da Matemática. Sociedade Brasileira de Matemática, 2014.
[Wal73] P., Walters. Some results on the classification of non-invertible measure preserving transformations. In Recent advances in topological dynamics (Proc. Conf. Topological Dynamics, Yale Univ., New Haven, Conn., 1972; in honor of Gustav Arnold Hedlund), pages 266–276. Lecture Notes in Math., Vol. 318. Springer-Verlag, 1973.
[Wal75] P., Walters. A variational principle for the pressure of continuous transformations. Amer. J. Math., 97:937–971, 1975.
[Wal82] P., Walters. An introduction to ergodic theory. Springer-Verlag, 1982.
[Wey16] H., Weyl. Uber die Gleichverteilungen von Zahlen mod Eins. Math. Ann., 77:313–352, 1916.
[Yan80] K., Yano. A remark on the topological entropy of homeomorphisms. Invent. Math., 59:215–220, 1980.
[Yoc92] J.-C., Yoccoz. Travaux de Herman sur les tores invariants. Astérisque, 206:Exp. No. 754, 4, 311–344, 1992. Séminaire Bourbaki, Vol. 1991/92.
[Yom87] Y., Yomdin. Volume growth and entropy. Israel J. Math., 57:285–300, 1987.
[Yos68] K., Yosida. Functional analysis. Second edition. Die Grundlehren der mathematischen Wissenschaften, Band 123. Springer-Verlag, 1968.
[Yuz68] S. A., Yuzvinskii. Metric properties of endomorphisms of compact groups. Amer. Math. Soc. Transl., 66:63–98, 1968.
[Zyg68] A., Zygmund. Trigonometric series: Vols. I, II. Second edition, reprinted with corrections and some additions. Cambridge University Press, 1968.