-
1
-
-
85033819420
-
-
note
-
In the physics community, this is referred to as "phase space" methods. To avoid confusion over signal phase, we use the term "state space."
-
-
-
-
2
-
-
12044249591
-
The Analysis of Observed Chaotic Data in Physical Systems
-
H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, "The Analysis of Observed Chaotic Data in Physical Systems," Rev. Mod. Phys. 65 (4), 1331-1392 (1993).
-
(1993)
Rev. Mod. Phys.
, vol.65
, Issue.4
, pp. 1331-1392
-
-
Abarbanel, H.D.I.1
Brown, R.2
Sidorowich, J.J.3
Tsimring, L.S.4
-
4
-
-
85033829968
-
-
note
-
Strictly speaking, the attractor is the mathematical topology upon which the signal trajectories reside.
-
-
-
-
5
-
-
0003290175
-
On the Dimension of the Compact Invariant Sets of Certain Nonlinear Maps
-
edited by D. Rand and L. S. Young, Lecture Notes in Mathematics 898 Springer-Verlag, Berlin
-
R. Mañe, "On the Dimension of the Compact Invariant Sets of Certain Nonlinear Maps," in Dynamical Systems and Turbulence, Warwick 1980, edited by D. Rand and L. S. Young, Lecture Notes in Mathematics 898 (Springer-Verlag, Berlin, 1981), p. 230.
-
(1981)
Dynamical Systems and Turbulence, Warwick 1980
, pp. 230
-
-
Mañe, R.1
-
6
-
-
0000779360
-
Detecting Strange Attractors in Turbulence
-
edited by D. Rand and L. S. Young, Lecture Notes in Mathematics 898 Springer-Verlag, Berlin
-
F. Takens, "Detecting Strange Attractors in Turbulence," in Dynamical Systems and Turbulence, Warwick 1980, edited by D. Rand and L. S. Young, Lecture Notes in Mathematics 898 (Springer-Verlag, Berlin, 1981), p. 366.
-
(1981)
Dynamical Systems and Turbulence, Warwick 1980
, pp. 366
-
-
Takens, F.1
-
8
-
-
34548696055
-
Independent coordinates for strange attractors from mutual information
-
A. M. Fraser and H. L. Swinney. "Independent coordinates for strange attractors from mutual information," Phys. Rev. A 33, 1134-1140 (1986).
-
(1986)
Phys. Rev. A
, vol.33
, pp. 1134-1140
-
-
Fraser, A.M.1
Swinney, H.L.2
-
9
-
-
0030061274
-
Nonlinear analysis of environmental distortions of continuous wave signals in the ocean
-
T. W. Frison, H. D. I. Abarbanel, J. Cembrola, and R. Katz, "Nonlinear analysis of environmental distortions of continuous wave signals in the ocean," J. Acoust. Soc. Am. 99, 1 (1996).
-
(1996)
J. Acoust. Soc. Am.
, vol.99
, pp. 1
-
-
Frison, T.W.1
Abarbanel, H.D.I.2
Cembrola, J.3
Katz, R.4
-
11
-
-
35949006791
-
Determining embedding dimension for phase-space reconstruction using a geometrical construction
-
M. B. Kennel, R. Brown, and H. D. I. Abarbanel, "Determining embedding dimension for phase-space reconstruction using a geometrical construction," Phys. Rev. A 45, 3403-3411 (1992).
-
(1992)
Phys. Rev. A
, vol.45
, pp. 3403-3411
-
-
Kennel, M.B.1
Brown, R.2
Abarbanel, H.D.I.3
-
12
-
-
0001576305
-
Local False Nearest Neighbors and Dynamical Dimensions from Observed Chaotic Data
-
H. D. I. Abarbanel and M. B. Kennel, "Local False Nearest Neighbors and Dynamical Dimensions from Observed Chaotic Data," Phys. Rev. E. 47, 3057-3068 (1993).
-
(1993)
Phys. Rev. E
, vol.47
, pp. 3057-3068
-
-
Abarbanel, H.D.I.1
Kennel, M.B.2
-
13
-
-
0040921240
-
Nonlinear Analysis of High Reynolds Number Flows over a Buoyant Axisymmetric Body
-
H. D. I. Abarbanel, R. Katz, J. Cembrola, T. Galib. and T. Frison "Nonlinear Analysis of High Reynolds Number Flows over a Buoyant Axisymmetric Body," Phys. Rev. E 49, 4003-4018 (1994).
-
(1994)
Phys. Rev. E
, vol.49
, pp. 4003-4018
-
-
Abarbanel, H.D.I.1
Katz, R.2
Cembrola, J.3
Galib, T.4
Frison, T.5
-
14
-
-
85033818730
-
Nonlinear Dynamics of the Great Salt Lake: System Identification and Prediction
-
in press
-
H. D. I. Abarbanel and U. Lall, "Nonlinear Dynamics of the Great Salt Lake: System Identification and Prediction," J. Climate (in press).
-
J. Climate
-
-
Abarbanel, H.D.I.1
Lall, U.2
-
15
-
-
35949018382
-
Ergodic theory of chaotic and strange attractors
-
J. P. Eckmann and D. Ruelle, "Ergodic theory of chaotic and strange attractors", Rev. Mod. Phys. 57(3), 617-656 (1985).
-
(1985)
Rev. Mod. Phys.
, vol.57
, Issue.3
, pp. 617-656
-
-
Eckmann, J.P.1
Ruelle, D.2
-
16
-
-
6444240297
-
-
J. P. Eckmann, S.O. Kamphorst, D. Ruelle, and S. Ciliberto, Phys. Rev. A 34, 4971 (1986).
-
(1986)
Phys. Rev. A
, vol.34
, pp. 4971
-
-
Eckmann, J.P.1
Kamphorst, S.O.2
Ruelle, D.3
Ciliberto, S.4
-
17
-
-
35949009462
-
Computing the Lyapunov Exponents of a Dynamical System from Observed Time Series
-
R. Brown, P. Bryant, and H. D. I. Abarbanel, "Computing the Lyapunov Exponents of a Dynamical System from Observed Time Series," Phys. Rev. A 43, 2787-2806 (1991).
-
(1991)
Phys. Rev. A
, vol.43
, pp. 2787-2806
-
-
Brown, R.1
Bryant, P.2
Abarbanel, H.D.I.3
-
18
-
-
0000339204
-
Variation of Lyapunov Exponents on a Strange Attractor
-
H. D. I. Abarbanel, R. Brown, and M. Kennel, "Variation of Lyapunov Exponents on a Strange Attractor," J. Nonlinear Sci. 1, 175-199 (1991).
-
(1991)
J. Nonlinear Sci.
, vol.1
, pp. 175-199
-
-
Abarbanel, H.D.I.1
Brown, R.2
Kennel, M.3
-
19
-
-
0040921241
-
True Lyapunov Exponents and Models of Chaotic Data
-
H. D. I. Abarbanel and M. M. Sushchik, "True Lyapunov Exponents and Models of Chaotic Data,", Int. J. Bifurcation Chaos 3, 543-550 (1993).
-
(1993)
Int. J. Bifurcation Chaos
, vol.3
, pp. 543-550
-
-
Abarbanel, H.D.I.1
Sushchik, M.M.2
-
20
-
-
34249834828
-
Local Lyapunov Exponents Computed from Observed Data
-
H. D. I. Abarbanel, R. Brown, and M. Kennel, "Local Lyapunov Exponents Computed from Observed Data," J. Nonlinear Sci. 2, 343-365 (1992).
-
(1992)
J. Nonlinear Sci.
, vol.2
, pp. 343-365
-
-
Abarbanel, H.D.I.1
Brown, R.2
Kennel, M.3
-
21
-
-
0000543733
-
A Multiplicative Ergodic Theorem. Lyapunov Characteristic Numbers for Dynamical Systems
-
V. I. Oseledec, "A Multiplicative Ergodic Theorem. Lyapunov Characteristic Numbers for Dynamical Systems," Tr. Mosk. Mat. Obsc. 199, 197 (1968); Moscow Math. Soc. 19, 197 (1968).
-
(1968)
Tr. Mosk. Mat. Obsc.
, vol.199
, pp. 197
-
-
Oseledec, V.I.1
-
22
-
-
0000543733
-
-
V. I. Oseledec, "A Multiplicative Ergodic Theorem. Lyapunov Characteristic Numbers for Dynamical Systems," Tr. Mosk. Mat. Obsc. 199, 197 (1968); Moscow Math. Soc. 19, 197 (1968).
-
(1968)
Moscow Math. Soc.
, vol.19
, pp. 197
-
-
-
23
-
-
0001640825
-
Chaotic behavior in mulitdimension difference equations
-
Springer-Verlag, Berlin
-
J. L. Kaplan and J. A. Yorke, "Chaotic behavior in mulitdimension difference equations," in Lecture Notes in Mathematics (Springer-Verlag, Berlin, 1979), Vol. 730, p. 228.
-
(1979)
Lecture Notes in Mathematics
, vol.730
, pp. 228
-
-
Kaplan, J.L.1
Yorke, J.A.2
-
24
-
-
34250950477
-
Dimension and ausseres Mass
-
F. Hausdorff, "Dimension and ausseres Mass," Math. Ann. 79, 157-179 (1918).
-
(1918)
Math. Ann.
, vol.79
, pp. 157-179
-
-
Hausdorff, F.1
-
25
-
-
40749093037
-
Measuring the Strangeness of Strange Attractors
-
P. Grassberger and I. Procaccia, "Measuring the Strangeness of Strange Attractors," Physica D 9, 189 (1983).
-
(1983)
Physica D
, vol.9
, pp. 189
-
-
Grassberger, P.1
Procaccia, I.2
-
27
-
-
0000201428
-
Noise Reduction in Chaotic Time Series Using Scaled Probabilistic Methods
-
P. F. Marteau and H. D. I. Abarbanel, "Noise Reduction in Chaotic Time Series Using Scaled Probabilistic Methods," J. Nonlinear Sci. 1, 313-343 (1991).
-
(1991)
J. Nonlinear Sci.
, vol.1
, pp. 313-343
-
-
Marteau, P.F.1
Abarbanel, H.D.I.2
|