The authors of this paper define the notion of sporadicity, in order to fill the gap between periodic and chaotic behavior in discrete dynamical systems. When the entropy per unit time is positive, the system is chaotic, while the vanishing of the entropy is a necessary condition for the system to be periodic or multiperiodic. They realize that there is an invariant allowing us to distinguish different dynamical behavior among systems with vanishing entropy, and this is the algorithmic complexity of A. Kolmogorov [Usp. Mat. Nauk 38, No. 4(232), 27–36 (1983; Zbl 0597.60002)] and G. J. Chaitin [Algorithmic information theory. Cambridge: Cambridge University Press (1987; Zbl 0655.68003)]. The algorithmic complexity mentioned above increases as \(n\) for chaotic systems and as \(\log n\) for periodic systems. They give examples to show that there exist dynamical systems with an intermediate behavior and call them sporadic systems. For these systems the algorithmic complexity grows as \(n^{\nu_ 0}(\log n)^{\nu_ 1}\) with \(0<\nu_ 0<1\) or \(\nu_ 0=1\) and \(\nu_ 1<0\) as \(n\to \infty\). In such systems, the logarithm of separation of initially nearby trajectories grows at the same rate. One example is provided by some particular countable Markov chains, which can be chaotic or sporadic according to the values of a real parameter. The other example is given by the intermittent systems \(x_{n+1}=x_ n+cx^ z_ n\pmod 1\) for \(z\geq 1\), defined by P. Manneville [J. Phys. 41, No. 11, 1235–1243 (1980)], which are chaotic for \(z<2\) but sporadic for \(z\geq 2\), in which case the above sporadicity exponent is given by \(\nu_ 0=1/(z-1)\).