Dynamics of the third order Lyness' difference equation

DOI10.1080/10236190701264735zbMath1129.39003arXivmath/0612407OpenAlexW3103394730MaRDI QIDQ5423628

Anna Cima, Víctor Mañosa, Armengol Gasull

Publication date: 24 October 2007

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

Full work available at URL: https://arxiv.org/abs/math/0612407

zbMATH Keywords

periodic orbitrotation numberfirst integraldiscrete dynamical systemcircle mapLyness' recurrenceTodd's recurrence

Mathematics Subject Classification ID

Related Items (18)

On 2- and 3-periodic Lyness difference equations ⋮ Periodic Orbits of Planar Integrable Birational Maps ⋮ On the Set of Periods of the 2-Periodic Lyness’ Equation ⋮ Real dynamics of integrable birational maps ⋮ Linear fractional recurrences: periodicities and integrability ⋮ Integrability and non-integrability of periodic non-autonomous Lyness recurrences ⋮ NONAUTONOMOUS TWO-PERIODIC GUMOVSKI–MIRA DIFFERENCE EQUATIONS ⋮ A general method for studying quadratic perturbations of the third-order Lyness difference equation ⋮ Studying discrete dynamical systems through differential equations ⋮ On the critical periods of perturbed isochronous centers ⋮ Dynamics of the third order Lyness' difference equation ⋮ On second-order rational difference equations, Part 2 ⋮ On third-order rational difference equations, part 1 ⋮ From discrete integrable equations to Laurent recurrences ⋮ Global behaviour of solutions of cyclic systems ofqorder 2 or 3 generalized Lyness' difference equations and of other more general equations of higher order ⋮ Results and conjectures about order \(q\) Lyness' difference equation \(u_{n+q}u_n=a+u_{n+q - 1}+ \dots +u_{n+1}\) in \(\mathbb R_{\ast}^+\), with a particular study of the case \(q=3\) ⋮ ON PERIODIC SOLUTIONS OF 2-PERIODIC LYNESS' EQUATIONS ⋮ Results and problems about solutions of perturbed Lyness' type orderkdifference equations in , with examples, and test of the efficiency of a quasi-Lyapunov function method

Cites Work

• Zeeman's monotonicity conjecture
• Invariants and related Liapunov functions for difference equations
• Some invariants for \(k\)th-order Lyness equation.
• On rational recursive sequences
• Studying discrete dynamical systems through differential equations
• DYNAMICS OF SOME RATIONAL DISCRETE DYNAMICAL SYSTEMS VIA INVARIANTS
• Global Behavior of the Solutions of Lyness' Difference Equation
• Invariant Curves and Focal Points in a Lyness Iterative Process
• Dynamics of the third order Lyness' difference equation
• Global periodicity and complete integrability of discrete dynamical systems

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