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Linear response in the intermittent family: Differentiation in a weighted $C^0$-norm
1. | Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU |
2. | Université de Brest, Laboratoire de Mathématiques de Bretagne Atlantique, CNRS UMR 6205, Brest, France |
References:
[1] |
W. Bahsoun, C. Bose and Y. Duan, Rigorous Pointwise approximations for invariant densities of nonuniformly expanding maps, Ergodic Theory and Dynamical Systems, 35 (2015), 1028-1044.
doi: 10.1017/etds.2013.91. |
[2] |
W. Bahsoun, S. Galatolo, I. Nisoli and X. Niu, A Rigorous Computational Approach to Linear Response, Available at http://arxiv.org/abs/1506.08661 |
[3] |
W. Bahsoun and S. Vaienti, Metastability of certain intermittent maps, Nonlinearity, 25 (2012), 107-124.
doi: 10.1088/0951-7715/25/1/107. |
[4] |
V. Baladi, On the susceptibility function of piecewise expanding interval maps, Comm. Math. Phy., 275 (2007), 839-859.
doi: 10.1007/s00220-007-0320-5. |
[5] |
V. Baladi, Linear response, or else, Available at http://arxiv.org/pdf/1408.2937v1.pdf |
[6] |
V. Baladi and D. Smania, Linear response formula for piecewise expanding unimodal maps, Nonlinearity, 21 (2008), 677-711.
doi: 10.1088/0951-7715/21/4/003. |
[7] |
V. Baladi and M. Todd, Linear response for intermittent maps, Comm. Math. Phy., 347, (2016), 857-874. |
[8] |
O. Butterley and C. Liverani, Smooth Anosov flows: Correlation spectra and stability, J. Mod. Dyn., 1 (2007), 301-322.
doi: 10.3934/jmd.2007.1.301. |
[9] |
D. Dolgopyat, On differentiability of SRB states for partially hyperbolic systems, Invent. Math., 155 (2004), 389-449.
doi: 10.1007/s00222-003-0324-5. |
[10] |
S. Gouëzel and C. Liverani, Banach spaces adapted to Anosov systems, Ergodic Theory Dynam. Systems, 26 (2006), 189-217.
doi: 10.1017/S0143385705000374. |
[11] |
A. Katok, G. Knieper, M. Pollicott and H. Weiss, Differentiability and analyticity of topological entropy for Anosov and geodesic flows, Invent. Math., 98 (1989), 581-597.
doi: 10.1007/BF01393838. |
[12] |
A. Korepanov, Linear response for intermittent maps with summable and nonsummable decay of correlations, Nonlinearity, 29 (2016), 1735-1754, Available at http://arxiv.org/abs/1508.06571.
doi: 10.1088/0951-7715/29/6/1735. |
[13] |
C. Liverani, Invariant measures and their properties. a functional analytic point of view, Dynamical systems., Part II, 185-237, Pubbl. Cent. Ric. Mat. Ennio Giorgi, Scuola Norm. Sup., Pisa, 2003. |
[14] |
C. Liverani, B. Saussol and S. Vaienti, A probabilistic approach to intermittency, Ergodic theory Dynam. System, 19 (1999), 671-685.
doi: 10.1017/S0143385799133856. |
[15] |
Y. Pomeau and P. Manneville, Intermittent transition to turbulence in dissipative dynamical systems, Comm. Math. Phys., 74 (1980), 189-197.
doi: 10.1007/BF01197757. |
[16] |
D. Ruelle, Differentiation of SRB states, Comm. Math. Phys., 187 (1997), 227-241.
doi: 10.1007/s002200050134. |
[17] |
L.-S. Young, Recurrence times and rates of mixing, Israel J. Math., 110 (1999), 153-188.
doi: 10.1007/BF02808180. |
show all references
References:
[1] |
W. Bahsoun, C. Bose and Y. Duan, Rigorous Pointwise approximations for invariant densities of nonuniformly expanding maps, Ergodic Theory and Dynamical Systems, 35 (2015), 1028-1044.
doi: 10.1017/etds.2013.91. |
[2] |
W. Bahsoun, S. Galatolo, I. Nisoli and X. Niu, A Rigorous Computational Approach to Linear Response, Available at http://arxiv.org/abs/1506.08661 |
[3] |
W. Bahsoun and S. Vaienti, Metastability of certain intermittent maps, Nonlinearity, 25 (2012), 107-124.
doi: 10.1088/0951-7715/25/1/107. |
[4] |
V. Baladi, On the susceptibility function of piecewise expanding interval maps, Comm. Math. Phy., 275 (2007), 839-859.
doi: 10.1007/s00220-007-0320-5. |
[5] |
V. Baladi, Linear response, or else, Available at http://arxiv.org/pdf/1408.2937v1.pdf |
[6] |
V. Baladi and D. Smania, Linear response formula for piecewise expanding unimodal maps, Nonlinearity, 21 (2008), 677-711.
doi: 10.1088/0951-7715/21/4/003. |
[7] |
V. Baladi and M. Todd, Linear response for intermittent maps, Comm. Math. Phy., 347, (2016), 857-874. |
[8] |
O. Butterley and C. Liverani, Smooth Anosov flows: Correlation spectra and stability, J. Mod. Dyn., 1 (2007), 301-322.
doi: 10.3934/jmd.2007.1.301. |
[9] |
D. Dolgopyat, On differentiability of SRB states for partially hyperbolic systems, Invent. Math., 155 (2004), 389-449.
doi: 10.1007/s00222-003-0324-5. |
[10] |
S. Gouëzel and C. Liverani, Banach spaces adapted to Anosov systems, Ergodic Theory Dynam. Systems, 26 (2006), 189-217.
doi: 10.1017/S0143385705000374. |
[11] |
A. Katok, G. Knieper, M. Pollicott and H. Weiss, Differentiability and analyticity of topological entropy for Anosov and geodesic flows, Invent. Math., 98 (1989), 581-597.
doi: 10.1007/BF01393838. |
[12] |
A. Korepanov, Linear response for intermittent maps with summable and nonsummable decay of correlations, Nonlinearity, 29 (2016), 1735-1754, Available at http://arxiv.org/abs/1508.06571.
doi: 10.1088/0951-7715/29/6/1735. |
[13] |
C. Liverani, Invariant measures and their properties. a functional analytic point of view, Dynamical systems., Part II, 185-237, Pubbl. Cent. Ric. Mat. Ennio Giorgi, Scuola Norm. Sup., Pisa, 2003. |
[14] |
C. Liverani, B. Saussol and S. Vaienti, A probabilistic approach to intermittency, Ergodic theory Dynam. System, 19 (1999), 671-685.
doi: 10.1017/S0143385799133856. |
[15] |
Y. Pomeau and P. Manneville, Intermittent transition to turbulence in dissipative dynamical systems, Comm. Math. Phys., 74 (1980), 189-197.
doi: 10.1007/BF01197757. |
[16] |
D. Ruelle, Differentiation of SRB states, Comm. Math. Phys., 187 (1997), 227-241.
doi: 10.1007/s002200050134. |
[17] |
L.-S. Young, Recurrence times and rates of mixing, Israel J. Math., 110 (1999), 153-188.
doi: 10.1007/BF02808180. |
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