The M-set of λ exp(z)/z has infinite area
AbstractIt is known that the Fatou set of the map exp(z)/zdefined on the punctured plane ℂ*is empty. We consider theM-set of λ exp(z)/zconsisting of all parameters λ for which the Fatou set of λexp(z)/zis empty. We prove that theM-set of λexp(z)/zhas infinite area. In particular, the Hausdorff dimension of theM-set is 2. We also discuss the area of complement of theM-set.
2015 ◽
Vol 217
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pp. 133-159
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1985 ◽
Vol 39
(2)
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pp. 187-193
2000 ◽
Vol 122
(3)
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pp. 465-482
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Keyword(s):