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 \(q=3\)
DOI10.1155/2009/134749zbMath1177.39021OpenAlexW1991866252WikidataQ59220306 ScholiaQ59220306MaRDI QIDQ1034109
Publication date: 11 November 2009
Published in: Advances in Difference Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1155/2009/134749
invariant setslocal stabilityequilibriumdivergence2-periodic pointsLyness' difference equationpermanency
Multiplicative and other generalized difference equations (39A20) Stability theory for difference equations (39A30)
Related Items (2)
Cites Work
- 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
- 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
- Third-order integrable difference equations generated by a pair of second-order equations
- Global behavior of the solutions of thek-lacunary order 2kLyness' difference equation in , and of other more general equations
- DYNAMICS OF SOME RATIONAL DISCRETE DYNAMICAL SYSTEMS VIA INVARIANTS
- Some properties of thek-dimensional Lyness' map
- Global Behavior of the Solutions of Lyness' Difference Equation
- On Periodic Rational Difference Equations of Orderk
- Dynamics of the third order Lyness' difference equation
- Periodicity of some classes of holomorphic difference equations
- Some periodic and non-periodic recursions
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