Full Resolution of Smale’s 14th Problem

Establish the complete resolution of Smale’s 14th problem by rigorously characterizing the Lorenz attractor associated with the standard Lorenz ordinary differential equations dx/dt = σ(y − x), dy/dt = x(ρ − z) − y, dz/dt = xy − βz for positive parameters (σ, ρ, β), clarifying its existence, mathematical structure, and robustness within this flow.

Background

In the paper’s broader context, the author argues that the standard Lorenz equations possess three conserved quantities even in chaotic regimes, suggesting new angles from which classical questions about the Lorenz attractor might be revisited.

Within this discussion, the paper explicitly cites longstanding challenges in the field, naming Smale’s 14th problem as a classical open problem whose full resolution remains a target. The mention situates the paper’s findings as potentially relevant to the rigorous mathematical understanding of the Lorenz attractor.