The paper "The Dimension of Chaotic Attractors" by J. Doyne Farmer, Edward Ott, and James A. Yorke discusses the various definitions of dimension for chaotic attractors and their computational values. The authors explore two main types of dimensions: those that depend only on metric properties and those that depend on probabilistic properties (the frequency of trajectory visits to different regions of the attractor). They find that all probabilistic dimensions typically take on the same value, called the "dimension of the natural measure," while all metric dimensions typically take on a common value, called the "fractal dimension." The dimension of the natural measure is often equal to the Lyapunov dimension, which is defined in terms of Lyapunov numbers and is easier to compute. The authors conjecture that for typical chaotic attractors, the distribution of frequencies with which an orbit visits different regions is log-normal. They also present an example, the generalized Baker's transformation, to illustrate these concepts and compute the dimensions for this specific case. The paper concludes with a review of numerical experiments and relevant results, supporting the conjectures about the relationship between Lyapunov numbers and dimensions.The paper "The Dimension of Chaotic Attractors" by J. Doyne Farmer, Edward Ott, and James A. Yorke discusses the various definitions of dimension for chaotic attractors and their computational values. The authors explore two main types of dimensions: those that depend only on metric properties and those that depend on probabilistic properties (the frequency of trajectory visits to different regions of the attractor). They find that all probabilistic dimensions typically take on the same value, called the "dimension of the natural measure," while all metric dimensions typically take on a common value, called the "fractal dimension." The dimension of the natural measure is often equal to the Lyapunov dimension, which is defined in terms of Lyapunov numbers and is easier to compute. The authors conjecture that for typical chaotic attractors, the distribution of frequencies with which an orbit visits different regions is log-normal. They also present an example, the generalized Baker's transformation, to illustrate these concepts and compute the dimensions for this specific case. The paper concludes with a review of numerical experiments and relevant results, supporting the conjectures about the relationship between Lyapunov numbers and dimensions.