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Discrete versions of the Painleve equations (dPII and qPII) over finite fields are studied.
K. Okamoto, “Studies on the Painlevé equations I” Annali di Mathematica pura ed applicata
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B. Grammaticos, A. Ramani and V. Papageorgiou, Do integrable mappings have the Painlevé property?, Phys. Rev. Lett
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F.W. Nijhoff and V.G. Papageorgiou, Similarity reductions of integrable lattices and discrete analogues of the Painlevé II {\rm II} equation, Phys. Lett. A
1991
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A. Ramani, B. Grammaticos and J. Hietarinta, Discrete versions of the Painlevé equations, Phys. Rev. Lett
1991
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H. Sakai, Rational surfaces associated with affine root systems and geometry of the Painlevé equations, Comm. Math. Phys
2001
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T. Takenawa, Discrete dynamical systems associated with root systems of indefinite type, Comm. Math. Phys
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K. Kajiwara, M. Noumi and Y. Yamada, Discrete dynamical systems with W ( A m − 1 ( 1 ) × A n − 1 ( 1 ) ) W(A^{(1)}_{m-1}\times A^{(1)}_{n-1}) symmetry, Lett. Math. Phys
2002
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M.R. Murty, Introduction to p p -adic Analytic Number Theory
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A. Doliwa, M. Białecki and P. Klimczewski, The Hirota equation over finite fields: algebro-geometric approach and multisoliton solutions, J. Phys. A: Math. Gen
2003
Cited alongside, same era.
K. Kajiwara, T. Masuda, M. Noumi, Y. Ohta and Y. Yamada, Hypergeometric solutions to the q-Painlevé equations, Int. Math. Res. Not
2004
Cited alongside, same era.
T. Hamamoto, K. Kajiwara and N.S. Witte, Hypergeometric Solutions to the q-Painlevé Equation of Type ( A 1 + A 1 ′ ) ( 1 ) (A_{1}+A_{1}^{\prime})^{(1)} , Int. Math. Res. Not
2006
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J.H. Silverman, The Arithmetic of Dynamical Systems
2007
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J.A.G. Roberts, Order and symmetry in birational difference equations and their signatures over finite phase spaces, in Proc. Workshop Future Directions in Difference Equations
2011
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2012
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M. Kanki, J. Mada and T. Tokihiro, Discrete integrable equations over finite fields, SIGMA
2012
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J.A.G. Roberts and F. Vivaldi, Arithmetical method to detect integrability in maps, Phys. Rev. Lett
2005
Cited alongside, same era.
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M. Kanki, Integrability of discrete equations modulo a prime SIGMA
2013
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