There are several versions of the Kaplan-Yorke conjecture, with many of the higher dimensional ones remaining unsettled. The original Kaplan-Yorke conjecture proposed that, for a two-dimensional mapping, the capacity dimension D equals the Kaplan-Yorke dimension D_(K Y), D = D_(K Y) = d_Lya = 1 + σ_1/σ_2,

capacity dimension | Kaplan-Yorke dimension | Lyapunov characteristic exponent | Lyapunov dimension