Sporadicity: Between periodic and chaotic dynamical behaviors

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Abstract
We define the class of sporadic dynamical systems as the systems where the algorithmic complexity of Kolmogorov [Kolmogorov, A. N. (1983) Russ. Math. Surv. 38, 29-40] and Chaitin [Chaitin, G. J. (1987) Algorithmic Information Theory (Cambridge Univ. Press, Cambridge, U.K.)] as well as the logarithm of separation of initially nearby trajectories grow as nv0(log n)v1 with 0 < v0 < 1 or v0 = 1 and v1 < 0 as time n → ∞. These systems present a behavior intermediate between the multiperiodic (v0 = 0, v1 = 1) and the chaotic ones (v0 = 1, v1 = 0). We show that intermittent systems of Manneville [Manneville, P. (1980) J. Phys. (Paris) 41, 1235-1243] as well as some countable Markov chains may be sporadic and, furthermore, that the dynamical fluctuations of these systems may be of Lévy9s type rather than Gaussian.