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Volumn 22, Issue 5, 2012, Pages 727-762

Theory and computation of covariant lyapunov vectors

Author keywords

Characteristic Lyapunov vectors; Covariant Lyapunov vectors; Forward and backward Lyapunov vectors; High dimensional chaos; Lyapunov analysis; Lyapunov exponents; Tangent space

Indexed keywords

HIGH-DIMENSIONAL CHAOS; LYAPUNOV ANALYSIS; LYAPUNOV EXPONENT; LYAPUNOV VECTORS; TANGENT SPACE;

EID: 84869880996     PISSN: 09388974     EISSN: 14321467     Source Type: Journal    
DOI: 10.1007/s00332-012-9126-5     Document Type: Article
Times cited : (165)

References (42)
  • 3
    • 44949289316 scopus 로고
    • Maximum hyperchaos in generalized hénon map
    • Baier, G., Klein, M.:Maximum hyperchaos in generalized Hénon map. Phys. Lett. A 151, 281-284 (1990
    • (1990) Phys. Lett. A , vol.151 , pp. 281-284
    • Baier, G.1    Klein, M.2
  • 5
    • 0018989294 scopus 로고
    • Lyapunov characteristic exponents for smooth dynamical systems and for hamiltonian systems: A method for computing all of them. Part i: Theory. Part ii: Numerical application
    • Benettin, G., Galgani, L., Giorgilli, A., Strelcyn, J.M.: Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: A method for computing all of them. Part I: theory. Part II: numerical application. Meccanica 15, 9-30 (1980
    • (1980) Meccanica , vol.15 , pp. 9-30
    • Benettin, G.1    Galgani, L.2    Giorgilli, A.3    Strelcyn, J.M.4
  • 7
    • 0029412335 scopus 로고
    • The singular-vector structure of the atmospheric global circulation
    • Buizza, R., Palmer, T.: The singular-vector structure of the atmospheric global circulation. J. Atmos. Sci. 52, 1434-1456 (1995
    • (1995) J. Atmos. Sci. , vol.52 , pp. 1434-1456
    • Buizza, R.1    Palmer, T.2
  • 8
    • 0027835599 scopus 로고
    • Computation of optimal unstable structures for a numerical weather prediction model
    • Buizza, R., Tribbia, J., Molteni, F., Palmer, T.: Computation of optimal unstable structures for a numerical weather prediction model. Tellus A 45, 388-407 (1993
    • (1993) Tellus A , vol.45 , pp. 388-407
    • Buizza, R.1    Tribbia, J.2    Molteni, F.3    Palmer, T.4
  • 9
    • 35949018382 scopus 로고
    • Ergodic theory of chaos and strange attractors
    • Eckmann, J.-P., Ruelle, D.: Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57, 617-656 (1985
    • (1985) Rev. Mod. Phys. , vol.57 , pp. 617-656
    • Eckmann, J.-P.1    Ruelle, D.2
  • 10
    • 0001753894 scopus 로고    scopus 로고
    • On the concept of stationary lyapunov basis
    • Ershov, S.V., Potapov, A.B.: On the concept of stationary Lyapunov basis. Physica D 118, 167-198 (1998
    • (1998) Physica D , vol.118 , pp. 167-198
    • Ershov, S.V.1    Potapov, A.B.2
  • 11
    • 0031474566 scopus 로고    scopus 로고
    • Adjoint sensitivity and finite-time normal mode disturbances during blocking
    • Frederiksen, J.S.: Adjoint sensitivity and finite-time normal mode disturbances during blocking. J. Atmos. Sci. 54, 1144-1165 (1997
    • (1997) J. Atmos. Sci. , vol.54 , pp. 1144-1165
    • Frederiksen, J.S.1
  • 12
    • 0000471425 scopus 로고
    • Comparision of different methods for computing lyapunov exponents
    • Geist, K., Parlitz, U., Lauterborn, W.: Comparision of different methods for computing Lyapunov exponents. Prog. Theor. Phys. 83, 875-893 (1990
    • (1990) Prog. Theor. Phys. , vol.83 , pp. 875-893
    • Geist, K.1    Parlitz, U.2    Lauterborn, W.3
  • 14
    • 0004236492 scopus 로고    scopus 로고
    • 3rd edn. The Johns Hopkins University Press, Baltimore
    • Golub, G.H., van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore (1996
    • (1996) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 17
    • 84870698549 scopus 로고    scopus 로고
    • Vychislenie pokazateley lyapunova dlya raspredelennyh sistem: Preimuschestva i nedostatki razlichnyh chislennyh metodov
    • Kuptsov, P.V.: Vychislenie pokazateley Lyapunova dlya raspredelennyh sistem: Preimuschestva i nedostatki razlichnyh chislennyh metodov. Izv. Vuz. Prik. Nelinejn. Din. 5 (2010).
    • Izv. Vuz. Prik. Nelinejn. Din. , vol.5 , pp. 2010
    • Kuptsov, P.V.1
  • 18
    • 84869867323 scopus 로고    scopus 로고
    • Computation of lyapunov exponents for spatially extended systems: Advantages and limitations of various numerical methods
    • (in Russian
    • Computation of Lyapunov exponents for spatially extended systems: Advantages and limitations of various numerical methods, Appl. Nonlinear Dyn. 5 (2010) (in Russian
    • (2010) Appl. Nonlinear Dyn. , vol.5
  • 19
    • 68949143116 scopus 로고    scopus 로고
    • Violation of hyperbolicity in a diffusive medium with local hyperbolic attractor
    • Kuptsov, P.V., Kuznetsov, S.P.: Violation of hyperbolicity in a diffusive medium with local hyperbolic attractor. Phys. Rev. E 80, 016205 (2009
    • (2009) Phys. Rev. E , vol.80 , pp. 016205
    • Kuptsov, P.V.1    Kuznetsov, S.P.2
  • 20
    • 77949709874 scopus 로고    scopus 로고
    • Strict and fussy mode splitting in the tangent space of the ginzburg-landau equation
    • Kuptsov, P.V., Parlitz, U.: Strict and fussy mode splitting in the tangent space of the Ginzburg-Landau equation. Phys. Rev. E 81, 036214 (2010
    • (2010) Phys. Rev. E , vol.81 , pp. 036214
    • Kuptsov, P.V.1    Parlitz, U.2
  • 21
    • 34047095828 scopus 로고    scopus 로고
    • Hyperbolic attractor in a system of coupled non-autonomous van der pol oscillators: Numerical test for expanding and contracting cones
    • Kuznetsov, S.P., Sataev, I.R.: Hyperbolic attractor in a system of coupled non-autonomous van der Pol oscillators: numerical test for expanding and contracting cones. Phys. Lett. A 365, 97-104 (2007
    • (2007) Phys. Lett. A , vol.365 , pp. 97-104
    • Kuznetsov, S.P.1    Sataev, I.R.2
  • 23
    • 0000252343 scopus 로고    scopus 로고
    • A guide to lyapunov vectors
    • In: Palmer, T. (ed.), European Centre for Medium-Range Weather Forecasts, Reading
    • Legras, B., Vautard, R.: A guide to Lyapunov vectors. In: Palmer, T. (ed.) Predictability Seminar Proc., ECWF Seminar, vol. 1, pp. 135-146. European Centre for Medium-Range Weather Forecasts, Reading (1996
    • (1996) Predictability Seminar Proc., ECWF Seminar , vol.1 , pp. 135-146
    • Legras, B.1    Vautard, R.2
  • 24
    • 84940252991 scopus 로고
    • On the exponential solution of differential equations for a linear operator
    • Magnus, W.: On the exponential solution of differential equations for a linear operator. Commun. Pure Appl. Math. 7, 649-673 (1954
    • (1954) Commun. Pure Appl. Math. , vol.7 , pp. 649-673
    • Magnus, W.1
  • 25
    • 0000543733 scopus 로고
    • A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems
    • Oseledec, V.I.: A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems. Tr. Mosk. Mat. Ob○s. 19, 197-231 (1968
    • (1968) Tr. Mosk. Mat. Ob○s , vol.19 , pp. 197-231
    • Oseledec, V.I.1
  • 26
    • 0000543733 scopus 로고
    • Mosc. Math. Soc. 19, 197-231 (1968
    • (1968) Mosc. Math. Soc. , vol.19 , pp. 197-231
  • 28
    • 78651291264 scopus 로고    scopus 로고
    • Characteristic lyapunov vectors in chaotic time-delayed systems
    • Pazó, D., López, J.M.: Characteristic Lyapunov vectors in chaotic time-delayed systems. Phys. Rev. E 82, 056201 (2010
    • (2010) Phys. Rev. E , vol.82 , pp. 056201
    • Pazó, D.1    López, J.M.2
  • 29
    • 48349137636 scopus 로고    scopus 로고
    • Structure of characteristic lyapunov vectors in spatiotemporal chaos
    • Pazó, D., Szendro, I.G., López, J.M., Rodríguez, M.A.: Structure of characteristic Lyapunov vectors in spatiotemporal chaos. Phys. Rev. E 78, 016209 (2008
    • (2008) Phys. Rev. E , vol.78 , pp. 016209
    • Pazó, D.1    Szendro, I.G.2    López, J.M.3    Rodríguez, M.A.4
  • 30
    • 77249094114 scopus 로고    scopus 로고
    • Spatio-temporal evolution of perturbations in ensembles initialized by bred lyapunov and singular vectors
    • Pazó, D., Rodríguez, M.A., López, J.M.: Spatio-temporal evolution of perturbations in ensembles initialized by bred, Lyapunov and singular vectors. Tellus 62A, 10-23 (2010
    • (2010) Tellus , vol.62 A , pp. 10-23
    • Pazó, D.1    Rodríguez, M.A.2    López, J.M.3
  • 31
    • 0033387085 scopus 로고    scopus 로고
    • Convergence of singular vectors toward lyapunov vectors
    • Reynolds, C.A., Errico, R.M.: Convergence of singular vectors toward Lyapunov vectors. Mon. Weather Rev. 127, 2309-2323 (1999
    • (1999) Mon. Weather Rev. , vol.127 , pp. 2309-2323
    • Reynolds, C.A.1    Errico, R.M.2
  • 32
    • 51649166261 scopus 로고
    • Ergodic theory of differentiable dynamical systems
    • Ruelle, D.: Ergodic theory of differentiable dynamical systems. Publ. Math. IHÉS 50, 27-58 (1979
    • (1979) Publ. Math. IHÉS , vol.50 , pp. 27-58
    • Ruelle, D.1
  • 34
    • 0000672504 scopus 로고
    • A numerical approach to ergodic problem of dissipative dynamical systems
    • Shimada, I., Nagashima, T.: A numerical approach to ergodic problem of dissipative dynamical systems. Prog. Theor. Phys. 61, 1605-1616 (1979
    • (1979) Prog. Theor. Phys. , vol.61 , pp. 1605-1616
    • Shimada, I.1    Nagashima, T.2
  • 35
    • 34548431033 scopus 로고    scopus 로고
    • Spatiotemporal structure of lyapunov vectors in chaotic coupled-map lattices
    • Szendro, I.G., Pazó, D., Rodríguez, M.A., López, J.M.: Spatiotemporal structure of Lyapunov vectors in chaotic coupled-map lattices. Phys. Rev. E 76, 025202 (2007
    • (2007) Phys. Rev. E , vol.76 , pp. 025202
    • Szendro, I.G.1    Pazó, D.2    Rodríguez, M.A.3    López, J.M.4
  • 36
    • 0001509508 scopus 로고
    • Ensemble forecasting at nmc: The generation of perturbations
    • Toth, Z., Kalnay, E.: Ensemble forecasting at NMC: the generation of perturbations. Bull. Am. Meteorol. Soc. 74, 2317-2330 (1993
    • (1993) Bull. Am. Meteorol. Soc. , vol.74 , pp. 2317-2330
    • Toth, Z.1    Kalnay, E.2
  • 37
    • 0000593274 scopus 로고    scopus 로고
    • Ensemble forecasting at ncep and the breeding method
    • Toth, Z., Kalnay, E.: Ensemble forecasting at NCEP and the breeding method. Mon. Weather Rev. 125, 3297-3319 (1997
    • (1997) Mon. Weather Rev. , vol.125 , pp. 3297-3319
    • Toth, Z.1    Kalnay, E.2
  • 38
    • 0032004557 scopus 로고    scopus 로고
    • Periodic orbits, lyapunov vectors, and singular vectors in the lorenz system
    • Trevisan, A., Pancotti, F.: Periodic orbits, Lyapunov vectors, and singular vectors in the Lorenz system. J. Atmos. Sci. 55, 390-398 (1998
    • (1998) J. Atmos. Sci. , vol.55 , pp. 390-398
    • Trevisan, A.1    Pancotti, F.2
  • 39
    • 0026402437 scopus 로고
    • Short-time lyapunov exponent analysis and the transition to chaos in taylor-couette flow
    • Vastano, J.A., Moser, R.D.: Short-time Lyapunov exponent analysis and the transition to chaos in Taylor-Couette flow. J. Fluid Mech. 233, 83-118 (1991
    • (1991) J. Fluid Mech. , vol.233 , pp. 83-118
    • Vastano, J.A.1    Moser, R.D.2
  • 40
    • 34247265017 scopus 로고    scopus 로고
    • An efficient method for recovering lyapunov vectors from singular vectors
    • Wolfe, C.L., Samelson, R.M.: An efficient method for recovering Lyapunov vectors from singular vectors. Tellus A 59A, 355-366 (2007
    • (2007) Tellus A , vol.59 A , pp. 355-366
    • Wolfe, C.L.1    Samelson, R.M.2
  • 41
    • 78651301786 scopus 로고    scopus 로고
    • Comparison between covariant and orthogonal lyapunov vectors
    • Yang, H.-L., Radons, G.: Comparison between covariant and orthogonal Lyapunov vectors. Phys. Rev. E 82, 046204 (2010
    • (2010) Phys. Rev. E , vol.82 , pp. 046204
    • Yang, H.-L.1    Radons, G.2
  • 42
    • 61349143757 scopus 로고    scopus 로고
    • Hyperbolicity and the effective dimension of spatially-extended dissipative systems
    • Yang, H.-L., Takeuchi, K.A., Ginelli, F., Chaté, H., Radons, G.: Hyperbolicity and the effective dimension of spatially-extended dissipative systems. Phys. Rev. Lett. 102, 074102 (2009)
    • (2009) Phys. Rev. Lett. , vol.102 , pp. 074102
    • Yang, H.-L.1    Takeuchi, K.A.2    Ginelli, F.3    Chaté, H.4    Radons, G.5


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