We present a number of second order maps, which pass the singularity confinement test commonly used to identify integrable discrete systems, but which nevertheless are nonintegrable. As a more sensitive integrability test, we propose the analysis of the complexity (algebraic entropy) of the map using the growth of the degree of its iterates: integrability is associated with polynomial growth while the generic growth is exponential for chaotic systems.

• Received 1 December 1997

DOI:https://doi.org/10.1103/PhysRevLett.81.325