APPROXIMATE DESCRIPTION OF THE MANDELBROT SET. THERMODYNAMIC ANALOGY
Cite this article as:
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: https://doi.org/10.18500/0869-6632-2006-14-1-55-71
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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BibTeX
author = {O. B. Isaeva and Sergey P. Kuznetsov},
title = {APPROXIMATE DESCRIPTION OF THE MANDELBROT SET. THERMODYNAMIC ANALOGY},
year = {2006},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {14},number = {1},
url = {https://old-andjournal.sgu.ru/en/articles/approximate-description-of-the-mandelbrot-set-thermodynamic-analogy},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2006-14-1-55-71},pages = {55--71},issn = {0869-6632},
keywords = {-},
abstract = {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. }}