Escaping points and escaping parameters for singly periodic meromorphic maps: Hausdorff dimensions outlook

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Abstract
Let where R is a non-constant rational map. We prove that if is not an asymptotic value of f, then the Hausdorff dimension of the escaping set of f equals , where q is the maximal multiplicity of poles of f. We also consider the set of escaping parameters in the family , i.e. the parameters for which the orbit of a pre-pole of f escapes to infinity under iterates of . Under additional assumptions on f we prove that the Hausdorff dimension of the set of escaping parameters in the family is greater than or equal to .
Funding Information
  • National Science Center (2014/13/B/ST1/01033)
  • National Science Centre

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