The road to the discrete analogue of the Painlevé property: Nevanlinna meets singularity confinement

DOI10.1016/S0898-1221(03)00076-2zbMath1057.39018OpenAlexW2071921550MaRDI QIDQ1827160

K. M. Tamizhmani, T. Tamizhmani, Alfred Ramani, Basile Grammaticos

Publication date: 6 August 2004

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0898-1221(03)00076-2

zbMATH Keywords

discrete systemsPainlevé equationsmeromorphic functionssingularity confinementdiscrete integrabilityorder and Nevanlinna theory

Mathematics Subject Classification ID

Value distribution of meromorphic functions of one complex variable, Nevanlinna theory (30D35) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Discrete version of topics in analysis (39A12)

Related Items (7)

Results on solutions for several \(q\)-Painlevé difference equations concerning rational solutions, zeros, and poles ⋮ Unnamed Item ⋮ Quantum Painlevé equations: from continuous to discrete and back ⋮ On the Nevanlinna characteristic of \(f(z+\eta)\) and difference equations in the complex plane ⋮ Some properties about complex difference equations of Malmquist type ⋮ On the growth of logarithmic differences, difference quotients and logarithmic derivatives of meromorphic functions ⋮ Some properties of meromorphic solutions of \(q\)-difference equations

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