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Proceedings of the American Mathematical Society

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The differentiability of the hairs of $ {\rm exp}(Z)$


Author: M. Viana da Silva
Journal: Proc. Amer. Math. Soc. 103 (1988), 1179-1184
MSC: Primary 30D05; Secondary 58F08, 58F11
MathSciNet review: 955004
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Abstract: We prove that the hairs of the exponential-like maps $ f(z) = \lambda {e^z}$ are smooth curves. This answers affirmatively a question of Devaney and Krych. The proof is constructive in the sense that a dynamically defined $ {C^\infty }$ parametrization is presented.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0955004-1
Keywords: Exponential-like map, itinerary, hair, symbolic dynamics
Article copyright: © Copyright 1988 American Mathematical Society