DOI: 10.1016/s0294-1449(16)30110-x. Large deviation asymptotics for Anosov flows

Large deviation asymptotics for Anosov flows

10.1016/s0294-1449(16)30110-x

Crossref journal-article

European Mathematical Society - EMS - Publishing House GmbH

Annales de l'Institut Henri Poincaré C, Analyse non linéaire (2673)

Abstract

We derive precise asymptotic formulae for large deviation probabilities for suspensions of subshifts of finite type. As a corollary, we give a stronger version of the Central Limit Theorem. We apply our results to transitive Anosov flows, giving a result describing fluctuations in the volume of Bowen balls and an asymptotic large deviation formula of a homological nature involving Schwartzmann’s winding cycle.

Bibliography

Waddington, S. (1996). Large deviation asymptotics for Anosov flows. Annales de lâInstitut Henri PoincarÃ© C, Analyse Non LinÃ©aire, 13(4), 445â484.

Authors 1

Simon Waddington (first)

References 27 Referenced 24

10.2307/2373793 / Amer. J. Math. / Symbolic dynamics for hyperbolic flows by Bowen (1973)
{'year': '1975', 'series-title': 'Equilibrium states and the ergodic theory of Anosov diffeomorphisms', 'author': 'Bowen', 'key': '10.1016/S0294-1449(16)30110-X_bibB2'} / Equilibrium states and the ergodic theory of Anosov diffeomorphisms by Bowen (1975)
10.1007/BF01389848 / Invent. Math. / The ergodic theory of Axiom A flows by Bowen (1975)
10.1007/BF02937307 / Isr. J. Math. / Central limit asymptotics for shifts of finite type by Coelho (1990)
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.
10.1017/S0143385700002637 / Ergod. Th. and Dyn. Syst. / Approximation by Browian motion for Gibbs measures and flows under a function by Denker (1984)
10.24033/asens.1023 / Ann. Éc. Norm. / Généralisation du Théorème de Ikehara by Delange (1951)
{'year': '1985', 'series-title': 'Large Deviations and Statistical Mechanics', 'author': 'Ellis', 'key': '10.1016/S0294-1449(16)30110-X_bibE'} / Large Deviations and Statistical Mechanics by Ellis (1985)
{'key': '10.1016/S0294-1449(16)30110-X_bibGH', 'first-page': '73', 'article-title': 'Théorèmes limites pour une classe de chaines de Markov et applications aux difféomorphismes d’Anosov', 'volume': 'Vol. 24', 'author': 'Guivarc’h', 'year': '1988', 'journal-title': 'Ann. Inst. Henri Poincaré (Probabilitiés et Statistique)'} / Ann. Inst. Henri Poincaré (Probabilitiés et Statistique) / Théorèmes limites pour une classe de chaines de Markov et applications aux difféomorphismes d’Anosov by Guivarc’h (1988)
10.1090/S0002-9947-1990-1025756-7 / Trans. Amer. Math. Soc. / Large deviations in dynamical systems and stochastic processes by Kifer (1990)
10.1007/BF02699875 / Publ. Math. IHES / Closed orbits in homology classes by Katsuda (1990)
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. (10.1214/lnms/1215540317)
10.1016/0196-8858(87)90012-1 / Adv. Appl. Math. / Distribution of periodic orbits of symbolic and Axiom A flows by Lalley (1987)
10.1017/S0143385700002327 / Ergod. Th. and Dyn. Syst. / A complex Ruelle-Perron-Frobenius theorem and two counterexamples by Pollicott (1984)
10.1007/BF01388579 / Invent. Math. / On the rate of mixing of Axiom A flows by Pollicott (1985)
W. Parry and M. Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics, Asterisque, Vol. 187–188, Math. Soc. France, 1990.
10.1007/BF02757869 / Isr. J. Math. / The central limit theorem for geodesic flows on n-dimensional manifolds of negative curvature by Ratner (1973)
{'year': '1978', 'series-title': 'Thermodynamic Formalism', 'author': 'Ruelle', 'key': '10.1016/S0294-1449(16)30110-X_bibRul'} / Thermodynamic Formalism by Ruelle (1978)
{'key': '10.1016/S0294-1449(16)30110-X_bibRu2', 'first-page': '99', 'article-title': 'Resonances for Axiom A flows', 'volume': 'Vol. 25', 'author': 'Ruelle', 'year': '1987', 'journal-title': 'J. Diff. Geom.'} / J. Diff. Geom. / Resonances for Axiom A flows by Ruelle (1987)
10.2307/1969999 / Ann. of Math. / Asymptotic cycles by Schwartzmann (1957)
10.1007/BF01299384 / Monats. Math. / Prime orbit theorems with multidimensional constraints for Axiom A flows by Sharp (1992)
10.1017/S0143385700007434 / Ergod. Th. Dyn. Syst. / Closed orbits in homology classes for Anosov flows by Sharp (1993)
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. (10.1016/S0924-6509(08)70404-5)
{'key': '10.1016/S0294-1449(16)30110-X_bibT2', 'series-title': 'Probability theory and mathematical statistics (Kyoto 1986)', 'first-page': '482', 'author': 'Takahashi', 'year': '1988'} / Probability theory and mathematical statistics (Kyoto 1986) by Takahashi (1988)
D. V. Widder, The Laplace Transform, Princeton University University Press, 1946.
{'key': '10.1016/S0294-1449(16)30110-X_bibY', 'first-page': '525', 'article-title': 'Some large deviation results for dynamical systems', 'volume': 'Vol. 318', 'author': 'Young', 'year': '1990', 'journal-title': 'Trans. Amer. Math. Soc.'} / Trans. Amer. Math. Soc. / Some large deviation results for dynamical systems by Young (1990)
{'year': '1968', 'series-title': 'An Introduction to Harmonic Analysis', 'author': 'Katznelson', 'key': '10.1016/S0294-1449(16)30110-X_bibKa'} / An Introduction to Harmonic Analysis by Katznelson (1968)

Dates

Type	When
Created	8 years, 7 months ago (Feb. 2, 2017, 6:45 p.m.)
Deposited	10 months, 1 week ago (Oct. 21, 2024, 2:37 p.m.)
Indexed	10 months, 1 week ago (Oct. 22, 2024, 12:18 a.m.)
Issued	29 years, 1 month ago (Aug. 1, 1996)
Published	29 years, 1 month ago (Aug. 1, 1996)
Published Print	29 years, 1 month ago (Aug. 1, 1996)

Funders 0

None

BibTeX

@article{Waddington_1996, title={Large deviation asymptotics for Anosov flows}, volume={13}, ISSN={1873-1430}, url={http://dx.doi.org/10.1016/s0294-1449(16)30110-x}, DOI={10.1016/s0294-1449(16)30110-x}, number={4}, journal={Annales de l’Institut Henri Poincaré C, Analyse non linéaire}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Waddington, Simon}, year={1996}, month=aug, pages={445–484} }

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