Approximate Description of the Mandelbrot Set. Thermodynamic Analogy

Details Approximate Description of the Mandelbrot Set. Thermodynamic Analogy Approximate Description of the Mandelbrot Set. Thermodynamic Analogy

2005-04-29

arxiv.org/abs/nlin/0504063v1

Nonlinear Phenomena in Complex Systems, V.8, No.2, 2005

Nonlinear Sciences

Chaotic Dynamics

11 pages, 10 figures,3 tables

Scientific paper

Analogy between an approximate version of Feigenbaum 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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