Large deviation asymptotics for Anosov flows

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 13, Issue 4, 1996, Pages 445-484

  Waddington, S ^a  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ASONOV FLOW; ASYMPTOTIC BEHAVIOR; CENTRAL LIMIT THEOREM; FLUCTUATIONS; LARGE DEVIATION;

RANDOM PROCESSES;

EID: 0030352857     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(16)30110-X     Document Type: Article

References (27)

1. R. Bowen Symbolic dynamics for hyperbolic flows Amer. J. Math. Vol. 95 1973 429 460
2. R. Bowen Equilibrium states and the ergodic theory of Anosov diffeomorphisms LNM 470 1975 Springer Verlag Berlin-Heidelberg-New York
3. R. Bowen D. Ruelle The ergodic theory of Axiom A flows Invent. Math. Vol. 29 1975 181 202
4. Z. Coelho W. Parry Central limit asymptotics for shifts of finite type Isr. J. Math. Vol. 69 1990 235 249
5. 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.
6. M. Denker W. Philipp Approximation by Browian motion for Gibbs measures and flows under a function Ergod. Th. and Dyn. Syst. Vol. 4 1984 541 552
7. H. Delange Généralisation du Théorème de Ikehara Ann. Éc. Norm. Vol. 71 1951 213 242
8. R. Ellis Large Deviations and Statistical Mechanics 1985 Springer-Verlag New York, Berlin, Heidelberg
9. Y. Guivarc’h 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 73 98
10. Y. Kifer Large deviations in dynamical systems and stochastic processes Trans. Amer. Math. Soc. Vol. 321 1990 505 524
11. A. Katsuda T. Sunada Closed orbits in homology classes Publ. Math. IHES Vol. 71 1990 5 32
12. 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.
13. S. Lalley Distribution of periodic orbits of symbolic and Axiom A flows Adv. Appl. Math. Vol. 8 1987 154 193
14. M. Pollicott A complex Ruelle-Perron-Frobenius theorem and two counterexamples Ergod. Th. and Dyn. Syst. Vol. 4 1984 135 146
15. M. Pollicott On the rate of mixing of Axiom A flows Invent. Math. Vol. 81 1985 413 426
16. W. Parry and M. Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics, Asterisque , Vol. 187–188 , Math. Soc. France, 1990.
17. M. Ratner The central limit theorem for geodesic flows on n-dimensional manifolds of negative curvature Isr. J. Math. Vol. 16 1973 181 197
18. D. Ruelle Thermodynamic Formalism 1978 Addison Wesley New York
19. D. Ruelle Resonances for Axiom A flows J. Diff. Geom. Vol. 25 1987 99 116
20. S. Schwartzmann Asymptotic cycles Ann. of Math. Vol. 118 1957 270 284
21. R. Sharp Prime orbit theorems with multidimensional constraints for Axiom A flows Monats. Math. Vol. 114 1992 261 304
22. R. Sharp Closed orbits in homology classes for Anosov flows Ergod. Th. Dyn. Syst. Vol. 13 1993 387 408
23. 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.
24. Y. Takahashi Probability theory and mathematical statistics (Kyoto 1986) LNM 1299 1988 Springer Verlag Berlin-Heidelberg-New York 482 491
25. D. V. Widder, The Laplace Transform, Princeton University University Press, 1946.
26. L.S. Young Some large deviation results for dynamical systems Trans. Amer. Math. Soc. Vol. 318 1990 525 543
27. Y. Katznelson An Introduction to Harmonic Analysis 1968 Wiley New York