Large deviation asymptotics for Anosov flows

Simon Waddington

Annales de l'I.H.P. Analyse non linéaire (1996)

  • Volume: 13, Issue: 4, page 445-484
  • ISSN: 0294-1449

How to cite


Waddington, Simon. "Large deviation asymptotics for Anosov flows." Annales de l'I.H.P. Analyse non linéaire 13.4 (1996): 445-484. <>.

author = {Waddington, Simon},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {asymptotics; zeta function; large deviation probabilities; subshifts of finite type; Anosov flow; Ruelle operator},
language = {eng},
number = {4},
pages = {445-484},
publisher = {Gauthier-Villars},
title = {Large deviation asymptotics for Anosov flows},
url = {},
volume = {13},
year = {1996},

AU - Waddington, Simon
TI - Large deviation asymptotics for Anosov flows
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1996
PB - Gauthier-Villars
VL - 13
IS - 4
SP - 445
EP - 484
LA - eng
KW - asymptotics; zeta function; large deviation probabilities; subshifts of finite type; Anosov flow; Ruelle operator
UR -
ER -


  1. [B1] R. Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math., Vol. 95, 1973, pp. 429-460. Zbl0282.58009MR339281
  2. [B2] R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, LNM 470, Springer Verlag, Berlin-Heidelberg-New York, 1975. Zbl0308.28010MR442989
  3. [BR] R. Bowen and D. Ruelle, The ergodic theory of Axiom A flows, Invent. Math., Vol. 29, 1975, pp. 181-202. Zbl0311.58010MR380889
  4. [CP] Z. Coelho and W. Parry, Central limit asymptotics for shifts of finite type, Isr. J. Math., Vol. 69, 1990, pp. 235-249. Zbl0701.60026MR1045376
  5. [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. Zbl0769.60025
  6. [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. Zbl0554.60077MR779712
  7. [De] H. Delange, Généralisation du Théorème de Ikehara, Ann. Éc. Norm., Vol. 71, 1951, pp. 213-242. Zbl0056.33101MR68667
  8. [E] R. Ellis, Large Deviations and Statistical Mechanics, Springer-Verlag, New York, Berlin, Heidelberg, 1985. Zbl0567.60031MR814705
  9. [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. Zbl0649.60041MR937957
  10. [K] Y. Kifer, Large deviations in dynamical systems and stochastic processes, Trans. Amer. Math. Soc., Vol. 321, 1990, pp. 505-524. Zbl0714.60019MR1025756
  11. [Ka] Y. Katznelson, An Introduction to Harmonic Analysis, Wiley, New York, 1968. Zbl0169.17902MR248482
  12. [KS] A. Katsuda and T. Sunada, Closed orbits in homology classes, Publ. Math. IHES, Vol. 71, 1990, pp. 5-32. Zbl0728.58026MR1079641
  13. [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. Zbl0679.60034
  14. [La2] S. Lalley, Distribution of periodic orbits of symbolic and Axiom A flows, Adv. Appl. Math., Vol. 8, 1987, pp. 154-193. Zbl0637.58013MR886923
  15. [Po1] M. Pollicott, A complex Ruelle-Perron-Frobenius theorem and two counterexamples, Ergod. Th. and Dyn. Syst., Vol. 4, 1984, pp. 135-146. Zbl0575.47009MR758899
  16. [Po2] M. Pollicott, On the rate of mixing of Axiom A flows, Invent. Math., Vol. 81, 1985, pp. 413-426. Zbl0591.58025MR807065
  17. [PP] W. Parry and M. Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics, Asterisque, Vol. 187-188, Math. Soc. France, 1990. Zbl0726.58003MR1085356
  18. [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. Zbl0283.58010MR333121
  19. [Ru1] D. Ruelle, Thermodynamic Formalism, Addison Wesley, New York, 1978. MR511655
  20. [Ru2] D. Ruelle, Resonances for Axiom A flows, J. Diff. Geom., Vol. 25, 1987, pp. 99-116. Zbl0658.58026MR873457
  21. [Sc] S. Schwartzmann, Asymptotic cycles, Ann. of Math., Vol. 118, 1957, pp. 270-284. Zbl0207.22603MR88720
  22. [Sh1] R. Sharp, Prime orbit theorems with multidimensional constraints for Axiom A flows, Monats. Math., Vol. 114, 1992, pp. 261-304. Zbl0765.58025MR1203975
  23. [Sh2] R. Sharp, Closed orbits in homology classes for Anosov flows, Ergod. Th. Dyn. Syst., Vol. 13, 1993, pp. 387-408. Zbl0783.58059MR1235480
  24. [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. Zbl0553.60097MR780769
  25. [T2] Y. Takahashi, Probability theory and mathematical statistics (Kyoto 1986), pp. 482- 491, LNM 1299, Springer Verlag, Berlin-Heidelberg-New York, 1988. Zbl0656.60039
  26. [W] D.V. Widder, The Laplace Transform, Princeton University University Press, 1946. Zbl0063.08245MR5923JFM67.0384.01
  27. [Y] L.S. Young, Some large deviation results for dynamical systems, Trans. Amer. Math. Soc., Vol. 318, 1990, pp. 525-543. Zbl0721.58030

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.