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We investigate some of the discrete Painleve equations (dPII, qPI and qPII) and the discrete KdV equation over finite fields.
Okamoto, K., Studies on the Painlevé equations III, Math. Ann
1986
Earlier work this paper cites.
Okamoto, K., Studies on the Painlevé equations I, Annali di Mathematica pura ed applicata
1987
Earlier work this paper cites.
Okamoto, K., Studies on the Painlevé equations II, Japan J. Math
1987
Earlier work this paper cites.
Okamoto, K., Studies on the Painlevé equations IV, Funkcial. Ekvac. Ser. Int
1987
Earlier work this paper cites.
Quispel, G R W. Roberts, J A G. and Thompson, C J., Integrable mappings and soliton equations II, Physica D
1989
Earlier work this paper cites.
Ramani, A. Grammaticos, B. and Hietarinta, J., Discrete versions of the Painlevé equations, Phys. Rev. Lett
1991
Earlier work this paper cites.
Nijhoff, F W. and Papageorgiou, V G., Similarity reductions of integrable lattices and discrete analogues of the Painlevé II {\rm II} equation, Phys. Lett. A
1991
Earlier work this paper cites.
Grammaticos, B. Ramani, A. and Papageorgiou, V., Do integrable mappings have the Painlevé property?, Phys. Rev. Lett
1991
Earlier work this paper cites.
Ramani, A. Grammaticos, B. and Satsuma, J., Integrability of multidimensional discrete systems, Phys. Lett. A
1992
Cited alongside, same era.
Kajiwara, K. Yamamoto, K. and Ohta, Y., Rational solutions for discrete Painlevé II equation, Phys. Lett. A
1997
Cited alongside, same era.
Sakai, H., Rational surfaces associated with affine root systems and geometry of the Painlevé equations, Comm. Math. Phys
2001
Cited alongside, same era.
Takenawa, T., Discrete dynamical systems associated with root systems of indefinite type, Comm. Math. Phys
2001
Cited alongside, same era.
Murty, M R., Introduction to p p -adic Analytic Number Theory
2002
Cited alongside, same era.
Tamizhmani, K M. Tamizhmani, T. Grammaticos, B. and Ramani, A., Special Solutions for Discrete Painlevé Equations, in Discrete Integrable Systems
2004
Later among the works it cites.
Kajiwara, K. Masuda, T. Noumi, M. Ohta, Y. and Yamada, Y., Hypergeometric solutions to the q q -Painlevé equations, Int. Math. Res. Not
2004
Later among the works it cites.
Roberts, J A G. and Vivaldi, F., Signature of time-reversal symmetry in polynomial automorphisms over finite fields, Nonlinearity
2005
Later among the works it cites.
Hamamoto, T. Kajiwara, K. and Witte, N S., Hypergeometric Solutions to the q q -Painlevé Equation of Type ( A 1 + A 1 ′ ) ( 1 ) (A_{1}+A_{1}^{\prime})^{(1)} , Int. Math. Res. Not
2006
Later among the works it cites.
Silverman, J H., The Arithmetic of Dynamical Systems
2007
Later among the works it cites.
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2002
Cited alongside, same era.
Roberts, J A G. and Vivaldi, F., Arithmetical method to detect integrability in maps, Phys. Rev. Lett
2003
Cited alongside, same era.
Doliwa, A. Białecki, M. and Klimczewski, P., The Hirota equation over finite fields: algebro-geometric approach and multisoliton solutions, J. Phys. A: Math. Gen
2003
Cited alongside, same era.
Cited in the paper.
Roberts, J A G., Order and symmetry in birational difference equations and their signatures over finite phase spaces, Proceedings of the International Workshop Future Directions in Difference Equations
2011
Later among the works it cites.
Kanki, M. Mada, J. Tamizhmani, K M. and Tokihiro, T., Discrete Painlevé II equation over finite fields, J. Phys. A: Math. Theor
2012
Later among the works it cites.
Kanki, M. Mada, J. and Tokihiro, T., Discrete integrable equations over finite fields, SIGMA
2012
Later among the works it cites.