On the algebraic difference equations \(u_{n+2}+u_{n}=\psi (u_{n+1})\) in \(\mathbb R\), related to a family of elliptic quartics in the plane

DOI10.1016/j.jmaa.2006.02.095zbMath1114.39004OpenAlexW1989005614MaRDI QIDQ865301

Marc Rogalski, Guy Bastien

Publication date: 14 February 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.02.095

zbMATH Keywords

fixed pointinvariant curvesperiodsdiscrete dynamical systemrational difference equationWeierstrass' elliptic functions

Mathematics Subject Classification ID

Elliptic curves (14H52) Multiplicative and other generalized difference equations (39A20)

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Cites Work

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• On some algebraic difference equations \(u_{n+2} u_{n}= \psi(u_{n+1})\) in \(\mathbb R_*^+\), related to families of conics or cubics: generalization of the Lyness' sequences
• Zeeman's monotonicity conjecture
• Invariants and related Liapunov functions for difference equations
• On the integrability of correspondences associated to integral curves
• On the algebraic difference equations \(u_{n+2}u_n=\psi(u_{n+1})\) in \({\mathbb {R}^+_*}\), related to a family of elliptic quartics in the plane
• Global Behavior of the Solutions of Lyness' Difference Equation
• ELLIPTIC CURVES AND QUADRATIC RECURRENCE SEQUENCES
• Integrable mappings via rational elliptic surfaces

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