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We study a generic and paradigmatic two degrees of freedom system consistingof two coupled perturbed cat maps with different types of dynamics. The Wignerseparability entropy (WSE) -- equivalent to the operator space entanglemententropy -- and the classical separability entropy (CSE) are used as measures ofcomplexity. For the case where both degrees of freedom are hyperbolic, the mapsare classically ergodic and the WSE and the CSE behave similarly, growing up tohigher values than in the doubly elliptic case. However, when one map iselliptic and the other hyperbolic, the WSE reaches the same asymptotic valuethan that of the doubly hyperbolic case, but at a much slower rate. The CSEonly follows the WSE for a few map steps, revealing that classical dynamicalfeatures are not enough to explain complexity growth.

Quantum and classical complexity in coupled maps