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Feigenbaum Julia sets of singularities of free energy

Published online by Cambridge University Press:  13 October 2009

JIANYONG QIAO ,
YONGCHENG YIN  and
JUNYANG GAO
JIANYONG QIAO
Affiliation:
Center of Mathematics, China University of Mining and Technology (Beijing), Beijing 100083, China (email: qjy@cumtb.edu.cn, gjyyang@yahoo.com.cn)
YONGCHENG YIN
Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai, 200433, China (email: yin@zju.edu.cn)
JUNYANG GAO
Affiliation:
Center of Mathematics, China University of Mining and Technology (Beijing), Beijing 100083, China (email: qjy@cumtb.edu.cn, gjyyang@yahoo.com.cn)
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Abstract

Considering the Potts model on diamond-like hierarchical lattices, in this paper, we show that the Julia sets of the singularities of the free energy may be a Feigenbaum Julia set. Furthermore, we prove that these Julia sets are locally connected if they are connected.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 5 , October 2010 , pp. 1573 - 1591
Copyright
Copyright © Cambridge University Press 2009

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