On Fatou Sets Containing Baker Omitted Value

An omitted value of a transcendental meromorphic function f is called Baker value, in short bov if there disk D centered at the such that each component boundary $$f^{-1}(D)$$ bounded. Assuming Fatou set f, this article investigates dynamics function. Firstly, connectivity all components are determined. If U containing then it proved $$U'$$ infinitely connected and only lands on U, i.e. $$f^{k}(U') \subset U$$ for some $$k \ge 1$$ . Every other either simply or Herman ring. Further, assuming number critical points whose forward orbits do not intersect finite, we have shown belongs to finite set. This independent components. It completely invariant whenever invariant. an attracting domain compactly contains values Julia totally disconnected. domains be non-existent also that, 2-periodic (these ruled out when set), parabolic has no Some examples exhibiting different possibilities discussed. includes first example with which two