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Isaeva O. B., Kuznetsov S. P. Approximate description of the mandelbrot set. Thermodynamic analogy. Izvestiya VUZ. Applied Nonlinear Dynamics, 2006, vol. 14, iss. 1, pp. 55-71. DOI: 10.18500/0869-6632-2006-14-1-55-71

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Approximate description of the mandelbrot set. Thermodynamic analogy

Isaeva Olga Borisovna, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Kuznetsov Sergey Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences

Analogy between an approximate version of period-doubling (and period N-tupling) renormalization group analysis in complex domain and the phase transition theory of Yang-Lee (based on consideration of formally complexified thermodynamic values) is discussed. It is shown that the Julia sets of the renormalization transformation correspond to the approximation of Mandelbrot set of the original map. New aspects of analogy between the theory of dynamical systems and the phase transition theory are uncovered.

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