Chaotic dynamical systems are investigated, with the help of the R\'enyi information concept, both in their phase space and in their history space. Several phases are distinguished and their characteristics are discussed. Emphasis is put on two particular situations representing borderline cases of chaos: when an unstable periodic orbit exists in the system with a zero or an infinite Lyapunov exponent.
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Csordás et al. (1989) studied this question.
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