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The M-set of λ exp(z)/z has infinite area
Published online by Cambridge University Press: 11 January 2016
Abstract
It is known that the Fatou set of the map exp(z)/z defined on the punctured plane ℂ* is empty. We consider the M-set of λ exp(z)/z consisting of all parameters λ for which the Fatou set of λexp(z)/z is empty. We prove that the M-set of λexp(z)/z has infinite area. In particular, the Hausdorff dimension of the M-set is 2. We also discuss the area of complement of the M-set.
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- Research Article
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- Copyright © Editorial Board of Nagoya Mathematical Journal 2015
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