Large deviation asymptotics for Anosov flows
Waddington, Simon
Annales de l'I.H.P. Analyse non linéaire, Tome 13 (1996), p. 445-484 / Harvested from Numdam
Publié le : 1996-01-01
@article{AIHPC_1996__13_4_445_0,
     author = {Waddington, Simon},
     title = {Large deviation asymptotics for Anosov flows},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {13},
     year = {1996},
     pages = {445-484},
     mrnumber = {1404318},
     zbl = {0864.58038},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1996__13_4_445_0}
}
Waddington, Simon. Large deviation asymptotics for Anosov flows. Annales de l'I.H.P. Analyse non linéaire, Tome 13 (1996) pp. 445-484. http://gdmltest.u-ga.fr/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 339281 | Zbl 0282.58009

[B2] R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, LNM 470, Springer Verlag, Berlin-Heidelberg-New York, 1975. | MR 442989 | Zbl 0308.28010

[BR] R. Bowen and D. Ruelle, The ergodic theory of Axiom A flows, Invent. Math., Vol. 29, 1975, pp. 181-202. | MR 380889 | Zbl 0311.58010

[CP] Z. Coelho and W. Parry, Central limit asymptotics for shifts of finite type, Isr. J. Math., Vol. 69, 1990, pp. 235-249. | MR 1045376 | Zbl 0701.60026

[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 0769.60025

[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 779712 | Zbl 0554.60077

[De] H. Delange, Généralisation du Théorème de Ikehara, Ann. Éc. Norm., Vol. 71, 1951, pp. 213-242. | Numdam | MR 68667 | Zbl 0056.33101

[E] R. Ellis, Large Deviations and Statistical Mechanics, Springer-Verlag, New York, Berlin, Heidelberg, 1985. | MR 814705 | Zbl 0567.60031

[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 937957 | Zbl 0649.60041

[K] Y. Kifer, Large deviations in dynamical systems and stochastic processes, Trans. Amer. Math. Soc., Vol. 321, 1990, pp. 505-524. | MR 1025756 | Zbl 0714.60019

[Ka] Y. Katznelson, An Introduction to Harmonic Analysis, Wiley, New York, 1968. | MR 248482 | Zbl 0169.17902

[KS] A. Katsuda and T. Sunada, Closed orbits in homology classes, Publ. Math. IHES, Vol. 71, 1990, pp. 5-32. | Numdam | MR 1079641 | Zbl 0728.58026

[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 0679.60034

[La2] S. Lalley, Distribution of periodic orbits of symbolic and Axiom A flows, Adv. Appl. Math., Vol. 8, 1987, pp. 154-193. | MR 886923 | Zbl 0637.58013

[Po1] M. Pollicott, A complex Ruelle-Perron-Frobenius theorem and two counterexamples, Ergod. Th. and Dyn. Syst., Vol. 4, 1984, pp. 135-146. | MR 758899 | Zbl 0575.47009

[Po2] M. Pollicott, On the rate of mixing of Axiom A flows, Invent. Math., Vol. 81, 1985, pp. 413-426. | MR 807065 | Zbl 0591.58025

[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 1085356 | Zbl 0726.58003

[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 333121 | Zbl 0283.58010

[Ru1] D. Ruelle, Thermodynamic Formalism, Addison Wesley, New York, 1978. | MR 511655

[Ru2] D. Ruelle, Resonances for Axiom A flows, J. Diff. Geom., Vol. 25, 1987, pp. 99-116. | MR 873457 | Zbl 0658.58026

[Sc] S. Schwartzmann, Asymptotic cycles, Ann. of Math., Vol. 118, 1957, pp. 270-284. | MR 88720 | Zbl 0207.22603

[Sh1] R. Sharp, Prime orbit theorems with multidimensional constraints for Axiom A flows, Monats. Math., Vol. 114, 1992, pp. 261-304. | MR 1203975 | Zbl 0765.58025

[Sh2] R. Sharp, Closed orbits in homology classes for Anosov flows, Ergod. Th. Dyn. Syst., Vol. 13, 1993, pp. 387-408. | MR 1235480 | Zbl 0783.58059

[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 780769 | Zbl 0553.60097

[T2] Y. Takahashi, Probability theory and mathematical statistics (Kyoto 1986), pp. 482- 491, LNM 1299, Springer Verlag, Berlin-Heidelberg-New York, 1988. | Zbl 0656.60039

[W] D.V. Widder, The Laplace Transform, Princeton University University Press, 1946. | JFM 67.0384.01 | MR 5923 | Zbl 0063.08245

[Y] L.S. Young, Some large deviation results for dynamical systems, Trans. Amer. Math. Soc., Vol. 318, 1990, pp. 525-543. | Zbl 0721.58030