Author:
LEVIN GENADI,ŚWIA̧TEK GRZEGORZ
Abstract
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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
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