Permutable functions concerning differential equations

• Autores: X. Hua, Rémi Vaillancourt, X. L. Wang
• Localización: Journal of the Australian Mathematical Society, ISSN 1446-7887, Vol. 83, Nº 3, 2007, págs. 369-384
• Idioma: inglés
• DOI: 10.1017/s1446788700037988
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• Resumen

  • Let f and g be two permutable transcendental entire functions. Assume that f is a solution of a linear differential equation with polynomial coefficients. We prove that, under some restrictions on the coefficients and the growth of f and g, there exist two non-constant rational functions R1 and R2 such that R1(f)=R2(g). As a corollary, we show that f and g have the same Julia set: J(f)=J(g). As an application, we study a function f which is a combination of exponential functions with polynomial coefficients. This research addresses an open question due to Baker.