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P. Jung, J.G. Kissner, and P. Hänggi, Phys. Rev. Lett. 76, 3436 (1996); J. Łuczka, T. Czernik, and P. Hänggi, Phys. Rev. E 56, 3968 (1997); R. Bartussek, P. Hänggi, B. Lindner, and L. Schimansky-Geier, Physica D 109, 17 (1997); B. Lindner, L. Schimansky-Geier, P. Reimann, P. Hänggi, and M. Nagaoka, Phys. Rev. E 59, 1417 (1999).
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P. Jung, J.G. Kissner, and P. Hänggi, Phys. Rev. Lett. 76, 3436 (1996); J. Łuczka, T. Czernik, and P. Hänggi, Phys. Rev. E 56, 3968 (1997); R. Bartussek, P. Hänggi, B. Lindner, and L. Schimansky-Geier, Physica D 109, 17 (1997); B. Lindner, L. Schimansky-Geier, P. Reimann, P. Hänggi, and M. Nagaoka, Phys. Rev. E 59, 1417 (1999).
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Anomalous diffusion can be described in the framework of the fractional kinetic equation, which must be used instead of the usual diffusion equation, see, for instance, A.I. Saichev and G.M. Zaslavsky, Chaos 7, 753 (1997).
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note
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In general a dissipation term should be included together with the noise to exclude heating. The dissipation has to be rather weak to satisfy the Melnikov criterion [8] so that the chaotic layer persists.
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K.N. Alekseev, E.H. Cannon, J.C. McKinney, F.V. Kusmartsev, and D.K. Campbell, Phys. Rev. Lett. 80, 2669 (1998); Physica D 113, 129 (1998); K.N. Alekseev, M.V. Erementchouk, and F.V. Kusmartsev, Europhys. Lett. 47, 595 (1999).
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