Talk:Kaplan–Yorke conjecture

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Statement of the Conjecture

It should be specified *which* fractal dimension the Lyapunov dimension is conjectured to be equal to.

The original conjecture published by Kaplan & Yorke in the article "Chaotic Behavior of Multidimensional Difference Equations" is that the Lyapunov dimension is equal to what they define on page 215 using the box-counting dimension construction via open balls and on page 216 refer to as the "metric space dimension" and, erroneously, the "Hausdorff dimension". It is not clear that, in the case where the box-counting and Hausdorff dimensions differ, Kaplan and Yorke intend to conjecture one way or the other about which the Lyapunov dimension ought to equal. --Carterhinsley (talk) 06:45, 5 July 2024 (UTC)[reply]