Nonlinear Phenomena in Complex Systems, 2005, Vol.8, No.2, pp.157-165

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2005, Vol.8, No.2, pp.157-165

Complex Generalization of Approximate Renormalization Group Analysis and Mandelbrot Set. Thermodynamic Analogy.
O.B. Isaeva and S.P. Kuznetsov

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 are uncovered.
Key words: bifurcation, chaos, RG methode

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