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3
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85036376209
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T. Tél, in Directions in Chaos, edited by Bai-lin Hao (World Scientific, Singapore, 1990) Vol.3
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T. Tél, in Directions in Chaos, edited by Bai-lin Hao (World Scientific, Singapore, 1990) Vol.3
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4
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0004210476
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Bai-lin Hao, World Scientific, Singapore
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in STATPHYS 19, edited by Bai-lin Hao (World Scientific, Singapore, 1996).
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(1996)
STATPHYS 19
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5
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0003915006
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Cambridge University Press, Cambridge, England, and references therein
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Analyzing chaotic time series is such a rich field that even a partial list of the relevant papers is impossible here. See, for example, H. Kantz and T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, Cambridge, England, 1997), and references therein.
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(1997)
Nonlinear Time Series Analysis
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Kantz, H.1
Schreiber, T.2
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6
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0001085819
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We are only aware of the following paper on analyzing transient chaotic time series which focuses on the reconstruction of the vector space by using embedding: I.M. Jánosi and T. Tél, Phys. Rev. E 49, 2756 (1994).
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(1994)
Phys. Rev. E
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Jánosi, I.M.1
Tél, T.2
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7
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85036388597
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Chaos Focus Issue 3 (4) (1993)
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Chaos Focus Issue 3 (4) (1993).
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8
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24444476675
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S.W. McDonald, C. Grebogi, E. Ott, and J.A. Yorke, Physica D 17, 125 (1985).
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(1985)
Physica D
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McDonald, S.W.1
Grebogi, C.2
Ott, E.3
Yorke, J.A.4
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12
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0001587809
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Á. Péntek, Z. Toroczkai, T. Tél, C. Grebogi, and J. Yorke, Phys. Rev. E 51, 4076 (1995)
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(1995)
Phys. Rev. E
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Péntek, Á.1
Toroczkai, Z.2
Tél, T.3
Grebogi, C.4
Yorke, J.5
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14
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0000853548
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and references therein
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Z. Toroczkai, G. Károlyi, Á. Péntek, T. Tél, and C. Grebogi, Phys. Rev. Lett. 80, 500 (1998), and references therein.
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(1998)
Phys. Rev. Lett.
, vol.80
, pp. 500
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Toroczkai, Z.1
Károlyi, G.2
Péntek, Á.3
Tél, T.4
Grebogi, C.5
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16
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0001240852
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T. Morita, H. Hata, H. Mori, T. Horita, and K. Tomita, Prog. Theor. Phys. 78, 511 (1987)
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(1987)
Prog. Theor. Phys.
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Morita, T.1
Hata, H.2
Mori, H.3
Horita, T.4
Tomita, K.5
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18
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0000965724
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Phys. Rev. Lett.D. Auerbach, P. Cvitanović, J.-P. Eckmann, G.H. Gunaratne, and I. Procaccia, 58, 2387 (1988)
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(1988)
Phys. Rev. Lett.
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Auerbach, D.1
Cvitanović, P.2
Eckmann, J.-P.3
Gunaratne, G.H.4
Procaccia, I.5
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20
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0000878650
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P. Cvitanović, Focus Issue on Periodic Orbit Theory, Chaos 2, (1992)
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Phys. Rev. AD. Auerbach, 41, 6692 (1990);P. Cvitanović, Focus Issue on Periodic Orbit Theory, Chaos 2, (1992)
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Phys. Rev. A
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Auerbach, D.1
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22
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29444438680
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M. Dhamala and Y.-C. Lai (unpublished)
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C. Grebogi, E. Ott, and J.A. Yorke, Phys. Rev. A 37, 1711 (1988);M. Dhamala and Y.-C. Lai (unpublished).
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(1988)
Phys. Rev. A
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Grebogi, C.1
Ott, E.2
Yorke, J.A.3
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24
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0001024141
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Detection of unstable periodic orbits embedded in chaotic attractors has been an active area of investigation. For additional work besides Ref. 12, see, for example, G.B. Mindlin, X.-J. Hou, H.G. Solari, R. Gilmore, and N.B. Tufillaro, Phys. Rev. Lett. 64, 2350 (1990)
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(1990)
Phys. Rev. Lett.
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Mindlin, G.B.1
Hou, X.-J.2
Solari, H.G.3
Gilmore, R.4
Tufillaro, N.B.5
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30
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0001066377
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P. So, E. Ott, S.J. Schiff, D.T. Kaplan, T. Sauer, and C. Grebogi, Phys. Rev. Lett. 76, 4705 (1996)
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Phys. Rev. Lett.
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So, P.1
Ott, E.2
Schiff, S.J.3
Kaplan, D.T.4
Sauer, T.5
Grebogi, C.6
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34
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0003513785
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D. Rand, L. S. Young, Springer-Verlag, Berlin
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F. Takens, in Dynamical Systems and Turbulence, edited by D. Rand and L. S. Young, Lecture Notes in Mathematics Vol. 898 (Springer-Verlag, Berlin, 1981), p. 366
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Takens, F.1
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35949021230
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N.H. Packard, J.P. Crutchfield, J.D. Farmer, and R.S. Shaw, Phys. Rev. Lett. 45, 712 (1980).
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Phys. Rev. Lett.
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Packard, N.H.1
Crutchfield, J.P.2
Farmer, J.D.3
Shaw, R.S.4
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37
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0000390258
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The definition of the probability studied in that paper was, however, slightly different from the one considered in the present paper
-
The corresponding problem for chaotic attractors was discussed in X. Pei, K. Dolan, F. Moss, and Y.-C. Lai, Chaos 8, 853 (1998). The definition of the probability studied in that paper was, however, slightly different from the one considered in the present paper.
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(1998)
Chaos
, vol.8
, pp. 853
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Pei, X.1
Dolan, K.2
Moss, F.3
Lai, Y.-C.4
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41
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0000906011
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Y.-C. Lai, C. Grebogi, J.A. Yorke, and I. Kan, Nonlinearity 6, 779 (1993).
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Nonlinearity
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Lai, Y.-C.1
Grebogi, C.2
Yorke, J.A.3
Kan, I.4
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44
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0002870373
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Briefly, the method is as follows. Take a line segment intersecting the stable manifold in a region containing the chaotic saddle. Divide the line segment into a large number of subintervals and compute (Formula presented) the number of subintervals whose lifetimes under the inverse dynamics are larger than or equal to n, where the lifetime is the time within which a trajectory remains in the region. It was suggested that (Formula presented) scales with n as (Formula presented), where (Formula presented) is the topological entropy of the chaotic saddle [Q. Chen, E. Ott, and L.P. Hurd, Phys. Lett. A 156, 48 (1991)].
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(1991)
Phys. Lett. A
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, pp. 48
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Chen, Q.1
Ott, E.2
Hurd, L.P.3
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