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Oblique projection based stabilizing feedback for nonautonomous coupled parabolic-ode systems
Spectral estimates for Ruelle operators with two parameters and sharp large deviations
1. | Université de Bordeaux, Institut de Mathématiques de Bordeaux, 351, Cours de la Libération, 33405 Talence, France |
2. | University of Western Australia, Department of Mathematics and Statistics, 35 Stirling Highway, Perth WA 6009, Australia |
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 [
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R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lect. Notes in Maths. 470. Springer-Verlag, Berlin, 2008. |
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R. Bowen,
Symbolic dynamics for hyperbolic flows, Amer. J. Math., 95 (1973), 429-460.
doi: 10.2307/2373793. |
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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. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Encyclopedia of Mathematics and its Applications, 54. Cambridge Univ. Press, Cambridge, 1995.
doi: 10.1017/CBO9780511809187.![]() ![]() ![]() |
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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. |
show all references
References:
[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. Hasselblatt, Introduction 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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