Rigorous Classification of Lorenz Attractor Properties Across Parameter Regimes

Determine a rigorous classification of attractor properties in the standard Lorenz system across the parameter space of positive constants (σ, ρ, β), specifying for each regime the existence and qualitative nature of the system’s attractors and their dynamical characteristics.

Background

The paper claims the existence of conserved quantities for the Lorenz system and suggests that these may have implications for its global dynamics and bifurcation structure.

In this context, the author explicitly identifies the rigorous classification of attractor properties across parameter regimes as a classical open problem, highlighting the need for a comprehensive and mathematically precise map of the Lorenz system’s attractors over its parameter space.