Skip to main content
Have a personal or library account? Click to login
An efficient method for recovering Lyapunov vectors from singular vectors Cover

An efficient method for recovering Lyapunov vectors from singular vectors

Open Access
|Jan 2007

References

  1. Bennetin , G. , Galgani , L. , Giorgilli , A. and Strelcyn , J.-M. 1980 . Lya-punov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: A method for computing all of them . Meccanica 15 , 9 21 .
  2. Buizza , R. and Palmer , T. 1995 . The singular vector structure of the atmospheric general circulation. J. Atmos. Sc i . 52 , 1434 1456 .
  3. Buizza , R. , Houtekamer , P. L. , Toth , Z. , Pellerin , G. , Wei , M. and co-authors. 2005. A comparison of the ECMWF, MSC and NCEP global ensemble prediction systems. Mon. Wea. Rev . 133 , 1076 - 1097 .
  4. Coddington , E. A. and Levinson , N. 1955 . Theory of Ordinary Differential Equations . McGraw Hill , New York .
  5. Drazin , P. G. and Reid , W. H. 2004 . Hydrodynamical Stability . 2nd edition , Cambridge University Press , Cambridge, UK .
  6. Eckmann , J.-P. and Ruelle , D. 1985 . Ergodic theory of chaos and strange attractors . Rev. Mod. Phys . 57 , 617 656 .
  7. Farrell , B. F. 1989 . Optimal excitation of baroclinic waves. J. Atmos. Sc i . 46 , 1193 1206 .
  8. Farrell , B. F. and Ioannou , P. J. 1996 . Generalized stability theory part I: Autonomous operators. J. Atmos. Sc i . 53 , 2025 2040 .
  9. Frederilcsen , J. S. 1997 . Adjoint sensitivity and finite-time normal mode disturbances during blocking. J. Atmos. Sci . 54 , 1144 1165 .
  10. Goldhirsch , I. , Sulem , P. L. and Orszag , A. 1987 . Stability and lyapunov stability of dynamical systems: A differential approach and a numerical method . Phyisca D 27 , 311 337 .
  11. Golub , G. H. and Van Loan , C. F. 1996 . Matrix Computations 3rd edition The Johns Hopkins University Press Ltd , London .
  12. Legras , B. and Vautard , R. 1996 . A guide to Liapunov vectors . In: Predictability , Volume I. European Centre for Medium-Range Weather Forecasts , 143 156 .
  13. Lorenz , E. N. 1963 . Deterministic non-periodic flow. J. Atmos. Sc i . 20 , 130 141 .
  14. Lorenz , E. N. 1965 . A study of the predictability of a 28-variable atmospheric model . Tellus 17 , 321 333 .
  15. Lorenz , E. N. 1984 . The local structure of a chaotic attractor in four dimensions . Physica D 13 , 90 104 .
  16. Oseledec , V. 1968 . A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems . Trans. Moscow Math. Soc . 19 , 179 210 .
  17. Pedlosky , J. 1971 . Finite-amplitude baroclinic waves with small dissipation . J. Phys. Oceanogr 28 , 587 597 .
  18. Pedlosky , J. 1987 . Geophysical Fluid Dynamics . 2nd edition . Springer .
  19. Pedlosky , J. and Frenzen , C. 1980 . Chaotic and periodic behavior of finite-amplitude baroclinic waves. J. Atmos. Sci . 37 , 1177 1196 . New York .
  20. Samelson , R. M. 2001a . Lyapunov, floquet, and singular vectors for baroclinic waves. Nonlinear Processes Geophys. 8 , 439 - 448.
  21. Samelson , R. M. 2001b. Periodic orbits and disturbance growth for baroclinic waves. J. Atmos. Sc i . 58 , 436 450 .
  22. Samelson , R. M. and Wolfe , C. L. 2003 . A nonlinear baroclinic wave-mean oscillation with multiple normal mode instabilities. J. Atmos. Sc i . 60 , 1186 1199 .
  23. Shimada , I. and Nagashima , T. 1979 . A numerical approach to the ergodic problem of dissipative dynamical systems . Prog. Theor Phys . 61 , 1605 1616 .
  24. Sparrow , C. 1982 . The Lorenz Equations: Bifurcations , Chaos , and Strange Attractors. Springer-Verlag , New York .
  25. Trevisan , A. and Legnani , R. 1995 . Transient error growth and local predictability: A study of the Lorenz system . Tellus 47A , 103 117 .
  26. Trevisan , A. and Pancotti , F. 1998 . Periodic orbits, Lyapunov vectors, and singular vectors in the Lorenz system. J. Atmos. Sc i . 55 , 390 398 .
  27. Vannitsem , S. and Nicolis , C. 1997 . Lyapunov vectors and error growth patterns in a T21L3 quasigeostrophic model. J. Atmos. Sc i . 54 , 357 361 .
  28. Vastano , J. A. and Moser , R. D. 1991 . Short-time Lyapunov exponent analysis and the transition to chaos in Taylor-Couette flow . J. Fluid Mech . 233 , 83 118 .
  29. Wei , M. and Frederilcsen , J. S. 2004 . Error growth and dynamical vectors during southern hemisphere blocking . Nonlinear Processes Geophys . 11 , 99 118 .
  30. Wolfe , C. L. and Samelson , R. M. 2006 . Normal-mode analysis of a baroclinic wave-mean oscillation. J. Atmos. Sc i . 63 , 2795 2812 .
  31. Yoden , S. and Nomura , M. 1993 . Finite time lyapunov stability analysis and its application to atmospheric predictability. J. Atmos. Sc i . 50 , 1531 1543 .
Language: English
Page range: 355 - 366
Submitted on: May 24, 2006
Accepted on: Feb 2, 2007
Published on: Jan 1, 2007
Published by: Stockholm University Press
In partnership with: Paradigm Publishing Services

© 2007 Christopher L. Wolfe, Roger M. Samelson, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.