-
1
-
-
0001731208
-
Lyapunov exponents in chaotic systems: Their importance and their evaluation using observed data
-
Abarbanel, H. D. I., Brown, R. & Kennel, M. B. [1991] "Lyapunov exponents in chaotic systems: Their importance and their evaluation using observed data," Int. J. Mod. Phys. B5, 1347-1375.
-
(1991)
Int. J. Mod. Phys.
, vol.B5
, pp. 1347-1375
-
-
Abarbanel, H.D.I.1
Brown, R.2
Kennel, M.B.3
-
2
-
-
12044249591
-
The analysis of observed chaotic data in physical systems
-
Abarbanel, H. D. I., Brown, R., Sidorowich, J. J. & Tsimring, L. S. [1993] "The analysis of observed chaotic data in physical systems," Rev. Mod. Phys. 65, 1331-1392.
-
(1993)
Rev. Mod. Phys.
, vol.65
, pp. 1331-1392
-
-
Abarbanel, H.D.I.1
Brown, R.2
Sidorowich, J.J.3
Tsimring, L.S.4
-
3
-
-
0001874180
-
Nongenericity of ωstability
-
Abraham, R. & Smale, S. [1968] "Nongenericity of ωstability," in Global Analysis I, Proc. Symp. Pure Math. A. M. S., Vol. 14, pp. 5-8.
-
(1968)
Global Analysis I, Proc. Symp. Pure Math. A. M. S.
, vol.14
, pp. 5-8
-
-
Abraham, R.1
Smale, S.2
-
4
-
-
0000252317
-
Obstructions to shadowing when a Lyapunov exponent fluctuates about zero
-
Dawson, S., Grebogi, C., Sauer, T. & Yorke, J. A. [1994] "Obstructions to shadowing when a Lyapunov exponent fluctuates about zero," Phys. Rev. Lett. 73, 1927-1930.
-
(1994)
Phys. Rev. Lett.
, vol.73
, pp. 1927-1930
-
-
Dawson, S.1
Grebogi, C.2
Sauer, T.3
Yorke, J.A.4
-
5
-
-
33750490125
-
Local Lyapunov exponents in chaotic systems
-
Eckhardt, B. & Yao, D. [1993] "Local Lyapunov exponents in chaotic systems," Physica D65, 100-108.
-
(1993)
Physica
, vol.D65
, pp. 100-108
-
-
Eckhardt, B.1
Yao, D.2
-
6
-
-
35949018382
-
Ergodic theory of chaos and strange attractors
-
Eckmann, J.-P. & Ruelle, D. [1985] "Ergodic theory of chaos and strange attractors," Rev. Mod. Phys. 57, 617-656.
-
(1985)
Rev. Mod. Phys.
, vol.57
, pp. 617-656
-
-
Eckmann, J.-P.1
Ruelle, D.2
-
7
-
-
0035883240
-
Accurate low-dimensional approximation of the linear dynamics of fluid flow
-
Farrell, B. F. & Ioannou, P. J. [2001] "Accurate low-dimensional approximation of the linear dynamics of fluid flow," J. Atmos. Sci. 58, 2771-2789.
-
(2001)
J. Atmos. Sci.
, vol.58
, pp. 2771-2789
-
-
Farrell, B.F.1
Ioannou, P.J.2
-
8
-
-
34250093291
-
Scaling laws for invariant measures on hyperbolic and non-hyperbolic attractors
-
Grassberger, P., Badii, R. & Politi, A. [1988] "Scaling laws for invariant measures on hyperbolic and non-hyperbolic attractors," J. Stat. Phys. 51, 135-178.
-
(1988)
J. Stat. Phys.
, vol.51
, pp. 135-178
-
-
Grassberger, P.1
Badii, R.2
Politi, A.3
-
9
-
-
0002591468
-
A two-dimensional mapping with a strange attractor
-
Hénon, M. [1976] "A two-dimensional mapping with a strange attractor," Commun. Math. Phys. 50, 69-77.
-
(1976)
Commun. Math. Phys.
, vol.50
, pp. 69-77
-
-
Hénon, M.1
-
10
-
-
0031170125
-
Homoclinic tangencies and non-normal Jacobians - Effects of noise in non-hyperbolic chaotic systems
-
Jaeger, L. & Kantz, H. [1997] "Homoclinic tangencies and non-normal Jacobians - effects of noise in non-hyperbolic chaotic systems," Physica D105, 79-96.
-
(1997)
Physica
, vol.D105
, pp. 79-96
-
-
Jaeger, L.1
Kantz, H.2
-
12
-
-
0001036009
-
A study of the predictability of a 28-variable atmospheric model
-
Lorenz, E. N. [1965] "A study of the predictability of a 28-variable atmospheric model," Tellus 17, 321-333.
-
(1965)
Tellus
, vol.17
, pp. 321-333
-
-
Lorenz, E.N.1
-
13
-
-
0000313555
-
Quantifying local predictability in phase space
-
Nese, J. M. [1989] "Quantifying local predictability in phase space," Physica D35, 237-250.
-
(1989)
Physica
, vol.D35
, pp. 237-250
-
-
Nese, J.M.1
-
14
-
-
84949405337
-
Non-uniform chaotic dynamics with implications to information processing
-
Nicolis, J. S., Meyer-Kress, G. & Haubs, G. [1983] "Non-uniform chaotic dynamics with implications to information processing," Z. Naturforsch. 38a, 1157-1169.
-
(1983)
Z. Naturforsch.
, vol.38 A
, pp. 1157-1169
-
-
Nicolis, J.S.1
Meyer-Kress, G.2
Haubs, G.3
-
15
-
-
0000543733
-
A multiplicative ergodic theorem: Lyapunov characteristic numbers for dynamical systems
-
Oseledec, V. I. [1968] "A multiplicative ergodic theorem: Lyapunov characteristic numbers for dynamical systems," Trans. Moscow Math. Soc. 19, 197-231.
-
(1968)
Trans. Moscow Math. Soc.
, vol.19
, pp. 197-231
-
-
Oseledec, V.I.1
-
16
-
-
0003582543
-
-
Cambridge Univerity Press, Cambridge
-
Ott, E. [1993] Chaos in Dynamical Systems (Cambridge Univerity Press, Cambridge).
-
(1993)
Chaos in Dynamical Systems
-
-
Ott, E.1
-
17
-
-
0035948072
-
Local low dimensionality of atmospheric dynamics
-
Patil, D. J., Hunt, B. R., Kalnay, E., Yorke, J. A. & Ott, E. [2001] "Local low dimensionality of atmospheric dynamics," Phys. Rev. Lett. 86, 5878-5881.
-
(2001)
Phys. Rev. Lett.
, vol.86
, pp. 5878-5881
-
-
Patil, D.J.1
Hunt, B.R.2
Kalnay, E.3
Yorke, J.A.4
Ott, E.5
-
18
-
-
0001078820
-
Characteristic distributions of finite-time Lyapunov exponents
-
Prasad, A. & Ramaswamy, R. [1999] "Characteristic distributions of finite-time Lyapunov exponents," Phys. Rev. E60, 2761-2766.
-
(1999)
Phys. Rev.
, vol.E60
, pp. 2761-2766
-
-
Prasad, A.1
Ramaswamy, R.2
-
19
-
-
0003153450
-
How long do numerical chaotic solutions remain valid?
-
Sauer, T., Grebogi, C. & Yorke, J. A. [1997] "How long do numerical chaotic solutions remain valid?" Phys. Rev. Lett. 79, 59-62.
-
(1997)
Phys. Rev. Lett.
, vol.79
, pp. 59-62
-
-
Sauer, T.1
Grebogi, C.2
Yorke, J.A.3
-
20
-
-
0000672504
-
A numerical approach to ergodic problem of dissipative dynamical systems
-
Shimada, I. & Nagashima, T. [1979] "A numerical approach to ergodic problem of dissipative dynamical systems," Prog. Th. Phys. 61, 1605-1616.
-
(1979)
Prog. Th. Phys.
, vol.61
, pp. 1605-1616
-
-
Shimada, I.1
Nagashima, T.2
-
21
-
-
0033427662
-
Uncertainty dynamics and predictability in chaotic systems
-
Smith, L. A., Ziehmann, C. & Fraedrich, K. [1999] "Uncertainty dynamics and predictability in chaotic systems," Q. J. R. Meteorol. Soc. 125, 2855-2886.
-
(1999)
Q. J. R. Meteorol. Soc.
, vol.125
, pp. 2855-2886
-
-
Smith, L.A.1
Ziehmann, C.2
Fraedrich, K.3
-
22
-
-
0001823409
-
Disentangling error and uncertainty: On the predictability of nonlinear systems
-
ed. Mees, A. (Birkhäuser, Basel), Chap. 2
-
Smith, L. A. [2000] "Disentangling error and uncertainty: On the predictability of nonlinear systems," in Nonlinear Dynamics and Statistics, ed. Mees, A. (Birkhäuser, Basel), Chap. 2, pp. 31-64.
-
(2000)
Nonlinear Dynamics and Statistics
, pp. 31-64
-
-
Smith, L.A.1
-
23
-
-
0000094552
-
Finite time Lyapunov exponent and advection-diffusion equation
-
Tang, X. Z. & Boozer, A. H. [1996] "Finite time Lyapunov exponent and advection-diffusion equation," Physica D95, 283-305.
-
(1996)
Physica
, vol.D95
, pp. 283-305
-
-
Tang, X.Z.1
Boozer, A.H.2
-
24
-
-
0001554548
-
Self-similar transport in incomplete chaos
-
Zaslavsky, G. M., Stevens, D. & Weitzner, H. [1993] "Self-similar transport in incomplete chaos," Phys. Rev. E48, 1683-1694.
-
(1993)
Phys. Rev.
, vol.E48
, pp. 1683-1694
-
-
Zaslavsky, G.M.1
Stevens, D.2
Weitzner, H.3
-
25
-
-
0000748798
-
Localized Lyapunov exponents and the prediction of predictability
-
Ziehmann, C., Smith, L. A. & Kurths, J. [2000] "Localized Lyapunov exponents and the prediction of predictability," Phys. Lett. A271, 237-251.
-
(2000)
Phys. Lett.
, vol.A271
, pp. 237-251
-
-
Ziehmann, C.1
Smith, L.A.2
Kurths, J.3
|