Julia set of λ exp(z)/z with real parameters λ

Guoping Zhan ()
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Guoping Zhan: Zhejiang University of Technology

Indian Journal of Pure and Applied Mathematics, 2017, vol. 48, issue 2, 271-283

Abstract: Abstract In this paper, we investigate the Julia set of the family λ exp(z)/z with real parameters λ. We look for what values of real parameters λ such that the Julia set of λ exp(z)/z does not coincide with the whole plane, and thus gives a complete classification for real parameters, which is similar to Jang’s result of a family of transcendental entire functions. Moreover, We also discuss the shape and size of Fatou sets and Julia sets of λ exp(z)/z with real parameters λ when the Julia sets are not the whole plane.

Keywords: Julia set; Fatou set; Hausdorff dimension; meromorphic function (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s13226-017-0225-8

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