A Cauchy Problem for an Ultrahyperbolic Equation by Kostomarov

By Kostomarov

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1989b; Kapitaniak et al. 1990; Feudel et al. 1995a; Glendinning 1998; Sturman 1999a; Glendinning et al. 2000; Osinga et al. 2001; Stark et al. 2002]. The logistic map has been considered by Witt, Feudel, and Pikovsky [1997]; Prasad, Mehra, and Ramaswamy [1997, 1998]; Negi, Prasad, and Ramaswamy [2000]; Khovanov, Khovanova, Anishchenko, and McClintock [2000a]; Kim, Lim, and Ott [2003b]; Lim and Kim [2005]; Kim and Lim [2005]. Venkatesan and Lakshmanan [2001] studied a cubic onedimensional map. Hunt and Ott [2001]; Kim et al.

In particular, following rational approximations may be a proper way to study quasiperiodically forced systems experimentally. Secondly, as we will see below, on the basis of rational approximations one can derive criteria which can be used to detect SNAs and to distinguish them from chaotic attractors. Looking at the phase portraits of SNAs in various examples of quasiperiodically forced systems it becomes obvious that it is rather difficult to sort out whether a particular attractor is smooth, but very wrinkled, strange nonchaotic, or strange chaotic.

1982a; Rand et al. 1982]. The method of rational approximations is quite useful from different perspectives. Firstly, from a physical viewpoint a distinction between rational and irrational numbers is rather subtle, as in an experiment (and even in numerics) one can hardly distinguish them. Thus it is quite helpful to have a description that deals with rational numbers only. In particular, following rational approximations may be a proper way to study quasiperiodically forced systems experimentally.

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