메뉴 건너뛰기




Volumn 23, Issue 4, 2010, Pages 909-922

A simple framework to justify linear response theory

Author keywords

[No Author keywords available]

Indexed keywords


EID: 77949684421     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/23/4/008     Document Type: Article
Times cited : (155)

References (50)
  • 2
    • 36348987164 scopus 로고    scopus 로고
    • Blended response algorithms for linear fluctuation-dissipation for complex nonlinear dynamical systems
    • Abramov R V and Majda A J 2007 Blended response algorithms for linear fluctuation-dissipation for complex nonlinear dynamical systems Nonlinearity 20 2793-821
    • (2007) Nonlinearity , vol.20 , pp. 2793-2821
    • Abramov, R.V.1    Majda, A.J.2
  • 3
    • 84867954551 scopus 로고    scopus 로고
    • New approximations and tests of linear fluctuation-response for chaotic nonlinear forced-dissipative dynamical systems
    • Abramov R V and Majda A J 2008 New approximations and tests of linear fluctuation-response for chaotic nonlinear forced-dissipative dynamical systems J. Nonlinear Sci. 18 303-41
    • (2008) J. Nonlinear Sci. , vol.18 , pp. 303-341
    • Abramov, R.V.1    Majda, A.J.2
  • 4
    • 65549103407 scopus 로고    scopus 로고
    • A new algorithm for low frequency climate response
    • Abramov R V and Majda A J 2009 A new algorithm for low frequency climate response J. Atmos. Sci. 66 286-309
    • (2009) J. Atmos. Sci. , vol.66 , pp. 286-309
    • Abramov, R.V.1    Majda, A.J.2
  • 5
    • 15944401206 scopus 로고    scopus 로고
    • Navier-Stokes equations: Controllability by means of low modes forcing
    • Agrachev A A and Sarychev A V 2005 Navier-Stokes equations: controllability by means of low modes forcing J. Math. Fluid Mech. 7 108-52
    • (2005) J. Math. Fluid Mech. , vol.7 , pp. 108-152
    • Agrachev, A.A.1    Sarychev, A.V.2
  • 7
    • 44949166500 scopus 로고    scopus 로고
    • Linear response despite critical points
    • Baladi V 2008 Linear response despite critical points Nonlinearity 21 T81-90
    • (2008) Nonlinearity , vol.21
    • Baladi, V.1
  • 8
    • 34548433206 scopus 로고    scopus 로고
    • Smooth Anosov flows: Correlation spectra and stability
    • Butterley O and Liverani C 2007 Smooth Anosov flows: correlation spectra and stability J. Mod. Dyn. 1 301-22
    • (2007) J. Mod. Dyn. , vol.1 , pp. 301-322
    • Butterley, O.1    Liverani, C.2
  • 9
    • 43049138826 scopus 로고    scopus 로고
    • Linear response formula for piecewise expanding unimodal maps
    • Baladi V and Smania D 2008 Linear response formula for piecewise expanding unimodal maps Nonlinearity 21 677-711
    • (2008) Nonlinearity , vol.21 , pp. 677-711
    • Baladi, V.1    Smania, D.2
  • 10
    • 21144471502 scopus 로고
    • On the spectra of randomly perturbed expanding maps
    • Baladi V and Young L-S 1993 On the spectra of randomly perturbed expanding maps Commun. Math. Phys. 156 355-85
    • (1993) Commun. Math. Phys. , vol.156 , pp. 355-385
    • Baladi, V.1    Young, L.-S.2
  • 12
    • 0842346767 scopus 로고    scopus 로고
    • On differentiability of SRB states for partially hyperbolic systems
    • Dolgopyat D 2004 On differentiability of SRB states for partially hyperbolic systems Invent. Math. 155 389-449
    • (2004) Invent. Math. , vol.155 , pp. 389-449
    • Dolgopyat, D.1
  • 14
    • 0035516434 scopus 로고    scopus 로고
    • Ergodicity for the Navier-Stokes equation with degenerate random forcing: Finite-dimensional approximation
    • W E and Mattingly J C 2001 Ergodicity for the Navier-Stokes equation with degenerate random forcing: finite-dimensional approximation Commun. Pure Appl. Math. 54 1386-402
    • (2001) Commun. Pure Appl. Math. , vol.54 , pp. 1386-1402
    • Mattingly, J.C.1
  • 15
    • 34547816534 scopus 로고    scopus 로고
    • Climate response using a three-dimensional operator based on the fluctuation-dissipation theorem
    • Gritsun A and Branstator G 2007 Climate response using a three-dimensional operator based on the fluctuation-dissipation theorem J. Atmos. Sci. 64 2558-75
    • (2007) J. Atmos. Sci. , vol.64 , pp. 2558-2575
    • Gritsun, A.1    Branstator, G.2
  • 16
    • 0038378803 scopus 로고    scopus 로고
    • Construction of the linear response operator of an atmospheric general circulation model to small external forcing
    • Gritsoun A S, Branstator G and Dymnikov V P 2002 Construction of the linear response operator of an atmospheric general circulation model to small external forcing Russ. J. Numer. Anal. Math. Modelling 17 399-416
    • (2002) Russ. J. Numer. Anal. Math. Modelling , vol.17 , pp. 399-416
    • Gritsoun, A.S.1    Branstator, G.2    Dymnikov, V.P.3
  • 17
    • 56849093930 scopus 로고    scopus 로고
    • Climate response of linear and quadratic functionals using the fluctuation-dissipation theorem
    • Gritsun A, Branstator G and Majda A 2008 Climate response of linear and quadratic functionals using the fluctuation-dissipation theorem J. Atmos. Sci. 65 2824-41
    • (2008) J. Atmos. Sci. , vol.65 , pp. 2824-2841
    • Gritsun, A.1    Branstator, G.2    Majda, A.3
  • 18
    • 0000827327 scopus 로고    scopus 로고
    • Barotropic atmosphere response to small external actions: Theory and numerical experiments
    • Gritsun A and Dymnikov V 1999 Barotropic atmosphere response to small external actions: Theory and numerical experiments Izv. Akad. Nauk. Fiz. Atmos. Okeana. Biol. 35 565-81
    • (1999) Izv. Akad. Nauk. Fiz. Atmos. Okeana. Biol. , vol.35 , pp. 565-581
    • Gritsun, A.1    Dymnikov, V.2
  • 20
    • 48749091873 scopus 로고    scopus 로고
    • Compact locally maximal hyperbolic sets for smooth maps: Fine statistical properties
    • Gouzel S and Liverani C 2008 Compact locally maximal hyperbolic sets for smooth maps: fine statistical properties J. Diff. Geom. 79 433-77
    • (2008) J. Diff. Geom. , vol.79 , pp. 433-477
    • Gouzel, S.1    Liverani, C.2
  • 21
    • 33847788674 scopus 로고    scopus 로고
    • Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing
    • Hairer M and Mattingly J C 2006 Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing Ann. Math. (2) 164 993-1032
    • (2006) Ann. Math. (2) , vol.164 , pp. 993-1032
    • Hairer, M.1    Mattingly, J.C.2
  • 22
    • 61849127765 scopus 로고    scopus 로고
    • Spectral gaps in Wasserstein distances and the 2D stochastic Navier-Stokes equations
    • Hairer M and Mattingly J C 2008 Spectral gaps in Wasserstein distances and the 2D stochastic Navier-Stokes equations Ann. Probab. 36 2050-91
    • (2008) Ann. Probab. , vol.36 , pp. 2050-2091
    • Hairer, M.1    Mattingly, J.C.2
  • 25
    • 79952008924 scopus 로고    scopus 로고
    • Asymptotic coupling and a weak form of Harris' theorem with applications to stochastic delay equations
    • at press (DOI:10.1007/S00440-009-0250-6)
    • Hairer M, Mattingly J C and Scheutzow M 2009 Asymptotic coupling and a weak form of Harris' theorem with applications to stochastic delay equations Probab. Theory Relat. Fields at press (DOI:10.1007/S00440-009-0250-6)
    • (2009) Probab. Theory Relat. Fields
    • Hairer, M.1    Mattingly, J.C.2    Scheutzow, M.3
  • 26
    • 0000762587 scopus 로고
    • Polynomial control systems
    • Jurdjevic V and Kupka I 1985 Polynomial control systems Math. Ann. 272 361-8
    • (1985) Math. Ann. , vol.272 , pp. 361-368
    • Jurdjevic, V.1    Kupka, I.2
  • 27
    • 0003862232 scopus 로고
    • (Grundlehren der Mathematischen Wissenschaften band 132) 2nd edn (Berlin: Springer)
    • Kato T 1976 Perturbation Theory for Linear Operators (Grundlehren der Mathematischen Wissenschaften band 132) 2nd edn (Berlin: Springer)
    • (1976) Perturbation Theory for Linear Operators
    • Kato, T.1
  • 32
    • 0016559683 scopus 로고
    • Climate response and fluctuation dissipation
    • Leith C 1975 Climate response and fluctuation dissipation J. Atmos. Sci. 32 2022-6
    • (1975) J. Atmos. Sci. , vol.32 , pp. 2022-2026
    • Leith, C.1
  • 34
    • 76249097159 scopus 로고    scopus 로고
    • High skill in low-frequency climate response through fluctuation dissipation theorems despite structural instability
    • Majda A J, Abramov R and Gershgorin B 2010 High skill in low-frequency climate response through fluctuation dissipation theorems despite structural instability Proc. Natl Acad. Sci. 107 581-6
    • (2010) Proc. Natl Acad. Sci. , vol.107 , pp. 581-586
    • Majda, A.J.1    Abramov, R.2    Gershgorin, B.3
  • 35
    • 0037249680 scopus 로고    scopus 로고
    • On nonlinear controllability of homogeneous systems linear in control
    • Melody J, Baar T and Bullo F 2003 On nonlinear controllability of homogeneous systems linear in control IEEE Trans. Autom. Control 48 139-43
    • (2003) IEEE Trans. Autom. Control , vol.48 , pp. 139-143
    • Melody, J.1    Baar, T.2    Bullo, F.3
  • 37
    • 77949738950 scopus 로고    scopus 로고
    • Low frequency climate response and fluctuation-dissipation theorems: Theory and practice
    • at press (DOI:10.1175/2009JAS3264.1)
    • Majda A, Gershgorin B and Yuan Y 2010 Low frequency climate response and fluctuation-dissipation theorems: theory and practice J. Atmos. Sci. at press (DOI:10.1175/2009JAS3264.1)
    • (2010) J. Atmos. Sci.
    • Majda, A.1    Gershgorin, B.2    Yuan, Y.3
  • 39
    • 77949669181 scopus 로고    scopus 로고
    • Linear response theory for statistical ensembles in complex systems with time periodic forcing
    • Majda A and Wang X 2010 Linear response theory for statistical ensembles in complex systems with time periodic forcing Commun. Math. Sci. 8 142-72
    • (2010) Commun. Math. Sci. , vol.8 , pp. 142-172
    • Majda, A.1    Wang, X.2
  • 41
    • 58149204320 scopus 로고    scopus 로고
    • The Malliavin calculus and related topics
    • 2nd edn (Berlin: Springer)
    • Nualart D 2006 The Malliavin calculus and related topics Probability and its Applications 2nd edn (Berlin: Springer)
    • (2006) Probability and Its Applications
    • Nualart, D.1
  • 42
    • 0035086606 scopus 로고    scopus 로고
    • A nonlinear dynamical perspective on model error: A proposal for non-local stochastic-dynamic parametrization in weather and climate prediction models
    • Palmer T 2001 A nonlinear dynamical perspective on model error: a proposal for non-local stochastic-dynamic parametrization in weather and climate prediction models Q. J. R. Meteorol. Soc. part B 127 279-304
    • (2001) Q. J. R. Meteorol. Soc. , vol.127 , pp. 279-304
    • Palmer, T.1
  • 43
    • 77949751361 scopus 로고    scopus 로고
    • Palmer T and Williams P (ed) (Cambridge: Cambridge University Press)
    • Palmer T and Williams P (ed) 2010 Stochastic Physics and Climate Modelling (Cambridge: Cambridge University Press)
    • (2010) Stochastic Physics and Climate Modelling
  • 45
    • 3042696292 scopus 로고    scopus 로고
    • Ergodicity of the finite dimensional approximation of the 3D Navier-Stokes equations forced by a degenerate noise
    • Romito M 2004 Ergodicity of the finite dimensional approximation of the 3D Navier-Stokes equations forced by a degenerate noise J. Stat. Phys. 114 155-77
    • (2004) J. Stat. Phys. , vol.114 , Issue.1-2 , pp. 155-177
    • Romito, M.1
  • 46
    • 0141774921 scopus 로고
    • The thermodynamic formalism for expanding maps
    • Ruelle D 1989 The thermodynamic formalism for expanding maps Commun. Math. Phys. 125 239-62
    • (1989) Commun. Math. Phys. , vol.125 , pp. 239-262
    • Ruelle, D.1
  • 47
    • 0031548918 scopus 로고    scopus 로고
    • Differentiation of SRB states
    • Ruelle D 1997 Differentiation of SRB states Commun. Math. Phys. 187 227-41
    • (1997) Commun. Math. Phys. , vol.187 , pp. 227-241
    • Ruelle, D.1
  • 48
    • 0023138986 scopus 로고
    • A general theorem on local controllability
    • Sussmann H J 1987 A general theorem on local controllability SIAM J. Control Optim. 25 158-94
    • (1987) SIAM J. Control Optim. , vol.25 , pp. 158-194
    • Sussmann, H.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.