Abstract
Analyzing the average over a year (a) and over a month (b) of Wolf numbers and radiocarbon data (c), we have obtained the dimensions d of the solar attractor which are: 3.3 (a), 4.3 (b), 4.7 (c). During the Maunder minimum such a dimension turns out to be significantly higher: 8.0 (c); whereas during the period of a phase catastrophe (1792–1828) Wolf numbers averaged over a month yield d = 3.0 (b). We have also investigated the sensitivity of our inferences to the number of available experimental points. Positive values of the Kolmogorov entropy and first Lyapunov exponent explicitly show the stochastic behaviour of the Sun.
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References
Aimanova, G. K. and Makarenko, N. G.: 1988, Astron. Tsirk. No. 1533 (in Russian).
Eddy, J. A.: 1976, Science 192, 1189.
Grassberger, P. and Procaccia, I.: 1983, Physica D9, 189.
Gudzenko, L. I. and Chertoprud, V. E.: 1980, Trudy P. N. Lebedev Fizich. Inst., AN SSSR 120, 167 (in Russian).
Kocharov, G. E., Vasiliev, V. A., Dergachev, V. A., and Ostryakov, V. M.: 1983, Pisma v Astron Zh. 9, 206 (in Russian).
Malinetzkii, G. G., Ruzmaikin, A. A., and Samarskii, A. A.: 1986, Preprint Inst. Prikl. Matem., AN SSSR, No. 170, p. 28 (in Russian).
Mayer-Kress, G.: 1987, in Hao Bai-Lin (ed.), ‘Directions in Chaos’, World Scientific Series on Directions in Condensed Matter Physics, Vol. 3, Singapore, p. 122.
Morfill, G. E. and Voges, W.: 1989, talk at The Sun in Time Conf., Tucson, Arizona.
Ostryakov, V. M. and Usoskin, I. G.: 1988, Soln. Dann. No. 2, 91 (in Russian).
Packard, N., Crutchfield, J. P., Farmer, J. D., and Shaw, R. S.: 1980, Phys. Rev. Letters 45, 712.
Ruzmaikin, A. A.: 1981, Comm. Astrophys. 9, 85.
Schuster, H. G.: 1984, Deterministic Chaos, Physic-Verlag, Weinheim.
Wolf, A., Swift, J. B., Swinney, H. L., and Vastano, J. A.: 1985, Physica D16, 285.
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Ostryakov, V.M., Usoskin, I.G. On the dimension of solar attractor. Sol Phys 127, 405–412 (1990). https://doi.org/10.1007/BF00152177
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DOI: https://doi.org/10.1007/BF00152177