Existence of standard map parameters with nonnegative Lyapunov exponent

Determine whether there exist values of the parameter in the standard map for which the Lyapunov exponent is nonnegative.

Background

In reviewing fundamental examples beyond uniformly hyperbolic systems, the authors highlight well-known challenges for non-uniformly hyperbolic dynamics such as the standard map. They point out a classical open question concerning the Lyapunov behavior of the standard map as a function of its parameter.

This serves as a representative example of difficult open problems in differentiable dynamical systems that are relevant to understanding computational capacity in complex dynamical regimes.