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Spectral estimates for Ruelle operators with two parameters and sharp large deviations

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  • We obtain spectral estimates for the iterations of Ruelle operators $ L_{f + (a + {\bf i} b)\tau + (c + {\bf i} d) g} $ with two complex parameters and Hölder continuous functions $ f,\: g $ generalizing the case $ {\rm{Pr}}(f) = 0 $ studied in [9]. As an application we prove a sharp large deviation theorem concerning exponentially shrinking intervals which improves the result in [8].

    Mathematics Subject Classification: Primary: 37C30; Secondary: 37D20, 37C35.


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  • [1] R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lect. Notes in Maths. 470. Springer-Verlag, Berlin, 2008.
    [2] R. Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math., 95 (1973), 429-460.  doi: 10.2307/2373793.
    [3] R. Bowen and D. Ruelle, The ergodic theory of Axiom A flows, Invent. Math., 29 (1975), 181-202.  doi: 10.1007/BF01389848.
    [4] D. Dolgopyat, Decay of correlations in Anosov flows, Ann. Math., 147 (1998), 357-390.  doi: 10.2307/121012.
    [5] A. Katok and  B. HasselblattIntroduction to the Modern Theory of Dynamical Systems, Encyclopedia of Mathematics and its Applications, 54. Cambridge Univ. Press, Cambridge, 1995.  doi: 10.1017/CBO9780511809187.
    [6] S. P. Lalley, Distribution of periodic orbits of symbolic and Axiom A flows, Adv. Appl. Math., 8 (1987), 154-193.  doi: 10.1016/0196-8858(87)90012-1.
    [7] W. Parry and M. Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics, Astérisque, (1990), 268 pp.
    [8] V. Petkov and L. Stoyanov, Sharp large deviations for some hyperbolic systems, Erg. Th. & Dyn. Sys., 35 (2015), 249-273. doi: 10.1017/etds.2013.48.
    [9] V. Petkov and L. Stoyanov, Ruelle transfer operators with two complex parameters and applications, Discr. Cont. Dyn. Sys. A, 36 (2016), 6413-6451. doi: 10.3934/dcds.2016077.
    [10] M. Pollicott and R. Sharp, Large deviations, fluctuations and shrinking intervals, Comm. Math. Phys., 290 (2009), 321-334.  doi: 10.1007/s00220-008-0725-9.
    [11] L. Stoyanov, Spectra of Ruelle transfer operators for Axiom A flows, Nonlinearity, 24 (2011), 1089-1120.  doi: 10.1088/0951-7715/24/4/005.
    [12] L. Stoyanov, Pinching conditions, linearization and regularity of Axiom A flows, Discr. Cont. Dyn. Sys. A, 33 (2013), 391-412.  doi: 10.3934/dcds.2013.33.391.
    [13] S. Waddington, Large deviations for Anosov flows, Ann. Inst. H. Poincaré, Analyse non-linéaire, 13 (1996), 445-484.  doi: 10.1016/S0294-1449(16)30110-X.
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