References
- Bastien , G and Rogalski , M . 2004 . Global behavior of the solutions of Lyness’ difference equation u n + 2 u n = u n+1 + a . J Differ Equ Appl , 10 : 977 – 1003 . doi: 10.1080/10236190410001728104
- Beukers , F and Cushman , R . 1998 . Zeeman’s monotonicity conjecture . J Differ Equations , 143 : 191 – 200 . doi: 10.1006/jdeq.1997.3359
- Esch , J and Rogers , T D . 2001 . The screensaver map: dynamics on elliptic curves arising from polygonal folding . Discrete Comput Geom , 25 : 477 – 502 . doi: 10.1007/s004540010075
- Zeeman , E C . 1996/2008 . Geometric unfolding of a difference equation , Hertford College . Unpublished paper. Reprinted as a Preprint of the Warwick Mathematics Institute
- Bastien , G and Rogalski , M . 2009 . Results and conjectures about order q Lyness’ difference Equation u n+q u n = a+u n+q − 1 + … + u n+1 in R + *, with a particular study of the case q = 3 . Adv Difference Equ , 2009 Article ID 134749 doi: 10.1155/2009/134749
- Camouzis , E and Ladas , G . 2008 . Dynamics of third-order rational difference equations with open problems and conjectures. Advances in discrete mathematics and applications. Vol. 5 , Boca Raton , FL : Chapman & Hall .
- Cima , A , Gasull , A and Mañosa , V . 2007 . Dynamics of the third order Lyness’ difference equation . J Differ Equ Appl , 13 : 855 – 844 . doi: 10.1080/10236190701264735
- Gao , M , Kato , Y and Ito , M . 2004 . Some invariants for kth-order Lyness equation . Appl Math Lett , 17 : 1183 – 1189 . doi: 10.1016/j.aml.2003.07.011
- Bastien , G , Mañosa , V and Rogalski , M . 2013 . On periodic solutions of 2-periodic Lyness difference equations . Int J Bifurcat Chaos , 23 : 1350071 doi: 10.1142/S0218127413500715
- Cima , A , Gasull , A and Mañosa , V . 2012 . On 2- and 3- periodic Lyness difference equations . J Differ Equ Appl , 18 : 849 – 864 . doi: 10.1080/10236198.2010.524212
- Feuer , J , Janowski , E J and Ladas , G . 1996 . Invariants for some rational recursive sequences with periodic coefficients . J Differ Equ Appl , 2 : 167 – 174 . doi: 10.1080/10236199608808051
- Janowski , E J , Kulenović , M RS and Nurkanović , Z . 2007 . Stability of the kth order Lyness’ equation with period–k coefficient . Int J Bifurcat Chaos , 17 : 143 – 152 . doi: 10.1142/S0218127407017227
- Kulenović , M RS and Nurkanović , Z . 2004 . Stability of Lyness’ equation with period–three coefficient . Radovi Matematički , 12 : 153 – 161 .
- Ramani , A , Grammaticos , B and Wilcox , R . 2011 . Generalized QRT mappings with periodic coefficients . Nonlinearity , 24 : 113 – 126 . doi: 10.1088/0951-7715/24/1/006
- Blanc , J . 2013 . Symplectic birational transformations of the plane . Osaka J Math , 50 : 573590
- Duistermaat , J J . 2010 . Discrete integrable systems: QRT maps and elliptic surfaces. Springer monographs in mathematics , New York , NY : Springer .
-
Usnich
,
A
.
Symplectic automorphisms of
and the Thomson group T , arXiv:math/0611604v3 [math.AG]
- Cima , A , Gasull , A and Mañosa , V . 2008 . Some properties of the k-dimensional Lyness map . J Phys A: Math Theor , 41 : 285205 doi: 10.1088/1751-8113/41/28/285205
- Grammaticos , B , Ramani , A and Tamizhmani , K M . 2009 . Investigating the integrability of the Lyness mappings . J Phys A: Math Theor , 42 : 454009 doi: 10.1088/1751-8113/42/45/454009
- Grammaticos , B , Ramani , A , Tamizhmani , K M and Wilcox , R . 2011 . On Quispel-Roberts-Thomson extensions and integrable correspondences . J Math Phys , 52 : 053508 doi: 10.1063/1.3588166
- Tran , D T , van der Kamp , P H and Quispel , G RW . 2010 . Sufficient number of integrals for the pth-order Lyness equation . J Phys A: Math Theor , 43 : 302001 doi: 10.1088/1751-8113/43/30/302001
- Arrowsmith , D K and Place , C M . 1990 . An introduction to dynamical systems , Cambridge University Press .
- de Angelis , V . 2005 . Notes on the non–autonomous Lyness equation . J Math Anal Appl , 307 : 292 – 304 . doi: 10.1016/j.jmaa.2004.10.046
- Li , W , Llibre , J and Zhang , X . 2001 . Planar analytic vector fields with generalized rational first integrals . Bull Sci Math , 125 : 341 – 361 . doi: 10.1016/S0007-4497(01)01083-1
- Grammaticos , B , Ramani , A and Tamizhmani , K M . 2011 . Mappings of Hirota-Kimura-Yahagi type can have periodic coefficients too . J Phys A: Math Theor , 44 : 015206 doi: 10.1088/1751-8113/44/1/015206
- Cima , A , Gasull , A and Mañosa , V . 2008 . Studying discrete dynamical systems through differential equations . J Differ Equations , 244 : 630 – 648 . doi: 10.1016/j.jde.2007.10.013
- Bastien , G and Rogalski , M . 2007 . On algebraic difference equations u n+2 + u n = ψ(u n+1) in related to a family of elliptic quartics in the plane . J Math Anal Appl , 326 : 822 – 844 . doi: 10.1016/j.jmaa.2006.02.095
- Cima , A and Zafar , S . Integrability and algebraic entropy of k-periodic non-autonomous Lyness recurrences . To appear in J Math Anal Appl ,