Measure of the Julia Set of the Feigenbaum map with infinite criticality

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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 go 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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General Topology, Dynamical Systems, 37F99

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http://salesiana.dossiersoluciones.com/handle/123456789/224383

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0705.0297
 http://arxiv.org/abs/0705.0297

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arXiv