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Measure of the Julia set of the Feigenbaum map with infinite criticality
Published online by Cambridge University Press: 29 June 2009
Abstract
We 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.
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- Copyright © Cambridge University Press 2009
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