Existence of analytic solutions to analytic nonlinear q-difference equations |
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Authors: | Xianyi Li Changgui Zhang |
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Institution: | a College of Mathematics and Computational Science, Shenzhen University, Shenzhen, Guangdong 518060, PR China b Laboratoire P. Painlevé, UFR Mathématique, Université de Lille 1, Cité Scientifique, 59655 Villeneuve d'Ascq, France |
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Abstract: | In this paper, some analytic approaches are formulated for the existence of analytic solutions of analytic nonlinear difference equations. From the point of view of dynamical systems, analytic solutions of such kinds of equations can be generally expressed by formal power series of exponential variables, so we are interested in considering a difference equation as a q-difference equation via a suitable coordinate transformation. After stating analytic results for formal series solutions of nonlinear q-difference equations, we also derive some results for the existence of analytic solutions to autonomous rational difference equations. |
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Keywords: | Difference equation Analytic solution Isomorphism Diffeomorphism Newton's polygon Poincaré domain |
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