hyperbolic dimension
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2009 ◽  
Vol 30 (3) ◽  
pp. 855-875 ◽  
Author(s):  
GENADI LEVIN ◽  
GRZEGORZ ŚWIA̧TEK

AbstractWe consider fixed points of the Feigenbaum (periodic-doubling) operator whose orders tend to infinity. It is known that the hyperbolic dimension of their Julia sets goes to 2. We prove that the Lebesgue measure of these Julia sets tend to zero. An important part of the proof consists in applying martingale theory to a stochastic process with non-integrable increments.


2007 ◽  
Vol 19 (01) ◽  
pp. 67-77 ◽  
Author(s):  
S. Buyalo ◽  
V. Schroeder

Nonlinearity ◽  
2006 ◽  
Vol 19 (12) ◽  
pp. 2877-2894 ◽  
Author(s):  
Neil Dobbs

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