Abstract
The “thermodynamic” formalism provides a very general division of strange (Cantor, fractal) sets into two classes; those which do exhibit phase transitions, and those which do not.
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References
R. Bowen, Lecture notes in Math. 470 (Springer, N.Y. 1975); D. Ruelle, “Statistical Mechanics, Thermodynamic Formalism”, Addision-Wesley, Reading (1978).
E. B. Vul, YaG. Sinai, and K. M. Khanin, Usp. Mat. Nauk. 39, 3 (1984) [Russ. Mat. Surveys 39, 1 (1984)].
T. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia and B. I. Shraiman, Phys. Rev. A33, 1141 (1986).
M. J. Feigenbaum, J. Stat. Phys. 46, 919 and 925 (1987).
P. Cvitanović, in Proceedings of the Workshop in Condensed Matter Physics”, Trieste, Italy 1986. (To be published); in R. Gilmore, ed., “Proceedings of the XV Int. Colloquium on Group Theoretical Methods in Physics” (World Scientific, Singapore, 1987).
R. Artuso, P. Cvitanovic and B. Kenny (to be published).
T. Tel, Phys. Rev. A36 (1987) to appear.
R. Badii, P. Grassberger and A. Politi (to be published).
T. Bohr and D. Rand, Physica 25D. 387 (1987).
T. Bohr and M. H. Jensen (to be published).
D. Katzen and I. Procaccia, Phys. Rev. Lett. 58, 1169 (1987).
P. Szépfalusy, T. Téi, A. Csordás and Kovács, preprint (1987).
P. Cvitanovic and G. Gunarathne (to be published).
P. Cvitanovic, G. Gunarathne and I. Procaccia (to be published).
P. Grassberger, Phys. Letters 107A. 101 (1985).
J. Balatoni and A. Renyi, Publi. Math. Inst. Hung. Acad. Sci. 1, 9 (1956) (english translation in The selected papers of A. Renvi. Vol. 1, p. 588 (Akademia Budapest, 1976)); A. Renyi, Probability Theory (appendix) (North- Holland, 1970).
H. G. Hentchel and I. Procaccia, Physica 8D, 435 (1983).
B. B. Madelbrot. J. Fluid Mech. 62, 331 (1974).
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© 1988 Plenum Press, New York
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Cvitanović, P. (1988). Phase Transitions on Strange Sets. In: Gallavotti, G., Zweifel, P.F. (eds) Nonlinear Evolution and Chaotic Phenomena. NATO ASI Series, vol 176. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1017-4_4
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DOI: https://doi.org/10.1007/978-1-4613-1017-4_4
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