Zeros, Poles, and Fixed Points of Meromorphic Solutions of Difference Painlevé Equations. (6th April 2014) - Lan, Shuang-Ting; Chen, Zong-Xuan
Abstract : In this paper, we mainly study the properties of transcendental meromorphic solutions f ( z ) of difference Painlevé equations w ( z + 1 ) w ( z - 1 ) ( w ( z ) - 1 ) = η ( z ) w 2 ( z ) - λ ( z ) w ( z ) and w ( z + 1 ) w ( z - 1 ) ( w ( z ) - 1 ) = η ( z ) w ( z ) and obtain precise estimations of the exponents of convergence of zeros, poles of Δ f ( z ) and Δ f ( z ) / f ( z ), and of fixed points of f ( z + c ) for any c ∈ ℂ .