Large deviation asymptotics for Anosov flows
Annales de l'I.H.P. Analyse non linéaire, Volume 13 (1996) no. 4, pp. 445-484.
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Waddington, Simon. Large deviation asymptotics for Anosov flows. Annales de l'I.H.P. Analyse non linéaire, Volume 13 (1996) no. 4, pp. 445-484. http://archive.numdam.org/item/AIHPC_1996__13_4_445_0/

[B1] R. Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math., Vol. 95, 1973, pp. 429-460. | MR | Zbl

[B2] R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, LNM 470, Springer Verlag, Berlin-Heidelberg-New York, 1975. | MR | Zbl

[BR] R. Bowen and D. Ruelle, The ergodic theory of Axiom A flows, Invent. Math., Vol. 29, 1975, pp. 181-202. | MR | Zbl

[CP] Z. Coelho and W. Parry, Central limit asymptotics for shifts of finite type, Isr. J. Math., Vol. 69, 1990, pp. 235-249. | MR | Zbl

[D] M. Denker, Large deviations and the pressure function. In: Transactions of the Eleventh Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, Czech Academy of Sciences, 1992, pp. 21-33. | Zbl

[DP] M. Denker and W. Philipp, Approximation by Browian motion for Gibbs measures and flows under a function, Ergod. Th. and Dyn. Syst., Vol. 4, 1984, pp. 541-552. | MR | Zbl

[De] H. Delange, Généralisation du Théorème de Ikehara, Ann. Éc. Norm., Vol. 71, 1951, pp. 213-242. | Numdam | MR | Zbl

[E] R. Ellis, Large Deviations and Statistical Mechanics, Springer-Verlag, New York, Berlin, Heidelberg, 1985. | MR | Zbl

[GH] Y. Guivarc'H and J. Hardy, Théorèmes limites pour une classe de chaines de Markov et applications aux difféomorphismes d'Anosov, Ann. Inst. Henri Poincaré (Probabilitiés et Statistique), Vol. 24, 1988, pp. 73-98. | Numdam | MR | Zbl

[K] Y. Kifer, Large deviations in dynamical systems and stochastic processes, Trans. Amer. Math. Soc., Vol. 321, 1990, pp. 505-524. | MR | Zbl

[Ka] Y. Katznelson, An Introduction to Harmonic Analysis, Wiley, New York, 1968. | MR | Zbl

[KS] A. Katsuda and T. Sunada, Closed orbits in homology classes, Publ. Math. IHES, Vol. 71, 1990, pp. 5-32. | Numdam | MR | Zbl

[La1] S. Lalley, Ruelle's Perron-Frobenius theorem and a central limit theorem for additive functionals of one-dimensional Gibbs states, Proc. Conf. in honour of H. Robbins, 1985. | Zbl

[La2] S. Lalley, Distribution of periodic orbits of symbolic and Axiom A flows, Adv. Appl. Math., Vol. 8, 1987, pp. 154-193. | MR | Zbl

[Po1] M. Pollicott, A complex Ruelle-Perron-Frobenius theorem and two counterexamples, Ergod. Th. and Dyn. Syst., Vol. 4, 1984, pp. 135-146. | MR | Zbl

[Po2] M. Pollicott, On the rate of mixing of Axiom A flows, Invent. Math., Vol. 81, 1985, pp. 413-426. | MR | Zbl

[PP] W. Parry and M. Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics, Asterisque, Vol. 187-188, Math. Soc. France, 1990. | MR | Zbl

[Ra] M. Ratner, The central limit theorem for geodesic flows on n-dimensional manifolds of negative curvature, Isr. J. Math., Vol. 16, 1973, pp. 181-197. | MR | Zbl

[Ru1] D. Ruelle, Thermodynamic Formalism, Addison Wesley, New York, 1978. | MR

[Ru2] D. Ruelle, Resonances for Axiom A flows, J. Diff. Geom., Vol. 25, 1987, pp. 99-116. | MR | Zbl

[Sc] S. Schwartzmann, Asymptotic cycles, Ann. of Math., Vol. 118, 1957, pp. 270-284. | MR | Zbl

[Sh1] R. Sharp, Prime orbit theorems with multidimensional constraints for Axiom A flows, Monats. Math., Vol. 114, 1992, pp. 261-304. | MR | Zbl

[Sh2] R. Sharp, Closed orbits in homology classes for Anosov flows, Ergod. Th. Dyn. Syst., Vol. 13, 1993, pp. 387-408. | MR | Zbl

[T1] Y. Takahashi, Entropy functional (free energy) for dynamical systems and their random perturbations. In: Stochastic analysis (Katata/Kyoto 1982), pp. 437-467, North Holland Math. Library 32, North Holland, Amsterdam-New York, 1984. | MR | Zbl

[T2] Y. Takahashi, Probability theory and mathematical statistics (Kyoto 1986), pp. 482- 491, LNM 1299, Springer Verlag, Berlin-Heidelberg-New York, 1988. | Zbl

[W] D.V. Widder, The Laplace Transform, Princeton University University Press, 1946. | JFM | MR | Zbl

[Y] L.S. Young, Some large deviation results for dynamical systems, Trans. Amer. Math. Soc., Vol. 318, 1990, pp. 525-543. | Zbl