Sporadicity: Between periodic and chaotic dynamical behaviors.
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 n(v(0) )(log n)(v(1) ) with 0 < v(0) < 1 or v(0) = 1 and v(1) < 0 as time n --> infinity. These systems present a behavior intermediate between the multiperiodic (v(0) = 0, v(1) = 1) and the chaotic ones (v(0) = 1, v(1) = 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 Lévy's type rather than Gaussian.
Université Libre de Bruxelles, Service de Chimie Physique II, Campus Plaine CP 231, Boulevard du Triomphe, B-1050 Brussels, Belgium.
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