References
- M.J. Ablowitz and P.A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge Unviersity Press, Cambridge, 1991.
- M.J. Ablowitz, R.G. Halburd, and B. Herbst, On the extension of the Painlevé property to difference equations, Nonlinearity 13 (2000), pp. 889–905.
- Y.M. Chiang and S.J. Feng, On the Nevanlinna characteristic of f (z + η) and difference equations in the complex plane, Ramanujan J. 16 (2008), pp. 105–129.
- B. Grammaticos, A. Ramani, and V. Papageorgiou, Do integrable mappings have the Painlevé property? Phys. Rev. Lett. 67 (1991), pp. 1825–1828.
- B. Grammaticos, T. Tamizhmani, A. Ramani, and K.M. Tamizhmani, Growth and integrability in discrete systems, J. Phys. A: Math. Gen. 34 (2001), pp. 3811–3821.
- V.I. Gromak, I. Laine, and S. Shimomura, Painlevé differential equations in the complex plane, Walter de Gruyter, Berlin, 2002.
- R.G. Halburd and R.J. Korhonen, Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations, J. Math. Anal. Appl. 314 (2006), pp. 477–487.
- R.G. Halburd and R.J. Korhonen, Finite order solutions and the discrete Painlevé equations, Proc. London Math. Soc. 94 (2007), pp. 443–474.
- R.G. Halburd and R.J. Korhonen, Meromorphic solutions of difference equations, integrability and the discrete Painlevé equations, J. Phys. A: Math. Theor. 40 (2007), pp. R1–R38.
- R.G. Halburd, R.J. Korhonen, and K. Tohge, Holomorphic curves with shift-invariant hyperplane preimages, preprint (2009). Available at arXiv: 0903.3236.
- W.K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964.
- K. Katajamäki, Algebroid solutions of binomial and linear differential equations, Ann. Acad. Sci. Fenn. Diss. 90 (1993), 48pp.
- R.J. Korhonen, A new clunie type theorem for difference polynomials, J. Differ. Equ. Appl. 17 (2011), pp. 387–400.
- I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin, 1993.
- I. Laine and C.C. Yang, Clunie theorems for difference and q-difference polynomials, J. Lond. Math. Soc. 76 (2007), pp. 556–566.
- S. Li and B.Q. Chen, Results on meromorphic solutions of linear difference equations, Adv. Differ. Equ. 2012 (2012), p. 203.
- N. Li and L.Z. Yang, Value distribution of certain type of difference polynomials, Abstract Appl. Anal. 2014 (2014), p. 278786.
- A.Z. Mohon’ko, The Nevanlinna characteristics of certain meromorphic functions, Teor. Funktsii Funktsional. Anal. i Prilozhen 14 (1971), pp. 83–87. Russian.
- A. Ramani, B. Grammaticos, and J. Hietarinta, Discrete versions of Painlevé equations, Phys. Rev. Lett. 67 (1991), pp. 1829–1832.
- O. Ronkainen, Meromorphic solutions of difference Painlevé equations, Ann. Acad. Sci. Fenn. Diss. 155 (2010), 59pp.
- G. Valiron, Sur la dérivée des fonctions algébroïdes [On the derivatives of algebroid functions], Bull. Soc. Math. France 59 (1931), pp. 17–39.
- C.C. Yang and H.X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht, 2003; Chinese original: Science Press, Beijing, 1995.
- J.L. Zhang, Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl. 367 (2010), pp. 401–408.
- J.L. Zhang, Meromorphic solutions of difference Painlevé IV equations, Adv. Differ. Equ. 2014 (2014), p. 260.