On determining the dimension of chaotic flows

Lorentz, 1963, J. Atmos. Sci., 20, 130, 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 Ruelle, 1976, Comm. Math. Phys., 50, 69, 10.1007/BF01609400 Huberman, 1979, Phys. Rev. Lett., 43, 1743, 10.1103/PhysRevLett.43.1743 Huberman, 1980, Appl. Phys. Lett., 37, 750, 10.1063/1.92020 Gollub, 1975, Phys. Rev. Lett., 35, 927, 10.1103/PhysRevLett.35.927 Walden, 1979, Phys. Rev. Lett., 42, 301, 10.1103/PhysRevLett.42.301 Rössler, 1976, Phys. Lett., 57A, 196 Packard, 1980, Phys. Rev. Lett., 45, 712, 10.1103/PhysRevLett.45.712 Roux, 1980, Phys. Lett., 77A, 391, 10.1016/0375-9601(80)90519-8 Shimada, 1979, Prog. Theor. Phys., 61, 1605, 10.1143/PTP.61.1605 Bennetin, 1976, Phys. Rev., A14, 2338, 10.1103/PhysRevA.14.2338 Mandelbrot, 1977 Eq. (2) defines a set's capacity, which we will take to be the same as the Haussdorf-Besicovitch dimension for the attractors we study. Mori, 1980, Prog. Theor. Phys., 63, 1044, 10.1143/PTP.63.1044 Farmer, 1980, Chaotic Attractors in Infinite-Dimensional Systems I: Differential Delay Equations Kaplan, 1979, Chaotic Behavior of Multidimensional Difference Equations, Springer Lecture Notes in Mathematics, 730, 204, 10.1007/BFb0064319 Crutchfield, 1979 Farmer, 1980, Annals, N.Y. Acad. Sci., 357, 453, 10.1111/j.1749-6632.1980.tb29710.x Williams, 1977, Berkeley Turbulence Seminar, 1976–1977, 615 Shaw, 1981, Z. Naturforsch., 36a, 80, 10.1515/zna-1981-0115 Abraham, 1976 D. Ruelle, private communication. Poincaré, 1913 Shepard, 1962, Psychometrika, 27, 125, 10.1007/BF02289630 Shepard, 1962, Psychometrika, 27, 219, 10.1007/BF02289621 Fukunaga, 1971, IEEE Trans. Comp., C-20, 176, 10.1109/T-C.1971.223208 Trunk, 1976, IEEE Trans. Comp., C-25, 165, 10.1109/TC.1976.5009231 White, 1974, Pattern Recognition, 6, 35, 10.1016/0031-3203(74)90006-5 Takens, 1980, Detecting Strange Attractors in Turbulence Hénon, 1976, Comm. Math. Phys., 50, 69, 10.1007/BF01608556 Simó, 1979, On the Hénon-Pomeau Attractor Rössler, 1979, Phys. Lett., 71A, 155, 10.1016/0375-9601(79)90150-6