Standard map parameter regimes with nonnegative Lyapunov exponent

Determine whether there exist parameter values of the Chirikov standard map for which the (largest) Lyapunov exponent is nonnegative, i.e., establish existence or non‑existence of such parameter regimes.

Background

The standard map is a canonical model for nonintegrable Hamiltonian dynamics and the onset of chaos. Despite extensive paper, key quantitative questions remain unresolved. The authors point to the status of Lyapunov exponents for the standard map as a representative difficult open problem in differentiable dynamics.

Clarifying whether any parameter values yield nonnegative Lyapunov exponents would sharpen understanding of the transition mechanisms between regular and chaotic behavior in area‑preserving maps.