Lebesgue measure of escaping sets of entire functions of completely regular growth

Abstract

We give conditions ensuring that the Julia set and the escaping set of an entire function of completely regular growth have positive Lebesgue measure. The essential hypotheses are that the indicator is positive except perhaps at isolated points and that most zeros are located in neighborhoods of finitely many rays. We apply the result to solutions of linear differential equations.

27 pages; Theorem 1.5 and its proof revised; some overall revision

References in corpus (2)

• Dynamics of meromorphic functions with direct or logarithmic singularities
• Hyperbolic dimension and radial Julia sets of transcendental functions

Cited by in corpus (2)

• Lebesgue measure of escaping sets of entire functions
• The escaping set in transcendental dynamics