Rigorous lower bounds for periods of general (non-symmetric) Lorenz orbits near T = 1.557

Ascertain whether rigorous lower bounds for the periods of general (non-symmetric) periodic orbits of the Lorenz system at parameters σ = 10, β = 8/3, ρ = 28 can be obtained that are close to T = 1.557, comparable to the near-sharp bounds achieved for symmetric orbits, using the auxiliary-function and sum-of-squares methodology.

Background

The paper successfully computes and validates near-sharp lower bounds for the periods of symmetric periodic orbits in the Lorenz system, matching the shortest known symmetric orbit to four decimal places. Extending such bounds to general (non-symmetric) orbits is substantially more challenging.

Using an approach similar to that developed for the Hénon–Heiles system, the authors were able to validate only T ≥ 0.98 for general Lorenz orbits, far from the suspected minimal period near 1.557, leaving the question of obtaining near-sharp bounds for general orbits unresolved.