Global behaviour of solutions of cyclic systems ofqorder 2 or 3 generalized Lyness' difference equations and of other more general equations of higher order

DOI10.1080/10236191003730555zbMath1247.37037OpenAlexW2060521042MaRDI QIDQ3103820

Guy Bastien, Marc Rogalski

Publication date: 12 December 2011

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10236191003730555

zbMATH Keywords

invariant setsdynamical systemsdifference equationsperiodsglobal behaviourglobal periodicitygeometric unfoldingLyness' equationsTodd's equations

Mathematics Subject Classification ID

Additive difference equations (39A10) Low-dimensional dynamical systems (37E99) Multiplicative and other generalized difference equations (39A20) Stability theory for difference equations (39A30)

Related Items (3)

Global behavior of solutions of the generalized Lyness difference equations under quadratic perturbations ⋮ On the periodicity of some classes of systems of nonlinear difference equations ⋮ A general method for studying quadratic perturbations of the third-order Lyness difference equation

Cites Work

• Unnamed Item
• 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
• 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
• Zeeman's monotonicity conjecture
• 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 thek-lacunary order 2kLyness' difference equation in , and of other more general equations
• Global Behavior of the Solutions of Lyness' Difference Equation
• Dynamics of the third order Lyness' difference equation

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