19 references, page 1 of 2

[1] M. Bellon and C-M. Viallet, Algebraic Entropy. Comm. Math. Phys. 204 (1999), pp. 425-437. chao-dyn/9805006.

[2] A.P. Veselov, Growth and Integrability in the Dynamics of Mappings. Comm. Math. Phys. 145 (1992), pp. 181-193. [OpenAIRE]

[3] G. Falqui and C.-M. Viallet, Singularity, complexity, and quasi-integrability of rational mappings. Comm. Math. Phys. 154 (1993), pp. 111-125. hep-th/9212105.

[4] G. Dimitrov, F. Haiden, L. Katzarkov, and M. Kontsevich. Dynamical systems and categories. arXiv:1307.841, (2013). [OpenAIRE]

[5] S. Tremblay, B. Grammaticos, and A. Ramani, Integrable lattice equations and their growth properties. Phys. Lett. A 278 (2001), pp. 319-324. [OpenAIRE]

[6] C-M. Viallet. Algebraic entropy for lattice equations. arXiv:math-ph/0609043.

[7] D.K. Demskoy and C.-M. Viallet, Algebraic entropy for semi-discrete equations. J. Phys. A: Math. Theor. 45 (2012), p. 352001. arXiv:1206.1214. [OpenAIRE]

[8] G.R.W. Quispel, H.W. Capel, and R. Sahadevan, Continous symmetries of differentialdifference equations: the Kac-van Moerbeke equation and the Painlev´e reduction. Phys. Lett. A(170) (1992), pp. 379-383.

[9] B. Grammaticos, A. Ramani, and I.C. Moreira, Delay-differential equations and the Painlev´e transcendents. Physica A 196 (1993), pp. 574-590.

[10] N. Joshi, Direct 'delay' reductions of the Toda equation. Journal of Physics A: Mathematical and Theoretical 42 (2009), pp. 022001-022009. arXiv:0810.5581.

[11] N. Joshi and P.E Spicer, Direct delay reductions of the Toda hierarchy. Journal of the Physical Society of Japan 78(9) (2009), p. 0940061 to 0940065. arXiv:0906.2169. [OpenAIRE]

[12] B. Grammaticos and A. Ramani. Integrability and how to detect it. In Y. KosmannSchwarzbach, B. Grammaticos, and K. M. Tamizhmani, editors, Integrability of nonlinear systems, Proceedings of the CIMPA School, number 495 in Lecture Notes in Physics, pages 30-94. Springer, (1997).

[13] B. Hasselblatt and J. Propp, Degree-growth of monomial maps. Ergodic Theory and Dynamical Systems 27(05) (2007), pp. 1375-1397. arXiv:math.DS/0604521.

[14] S.V. Manakov, Complete integrability and stochastization of discrete dynamical systems. Zh. Eksp. Teor Fiz 67 (1974), pp. 543-555. Sov. Phys. JETP, Vol. 40, No 2, pp 269-274.

[15] M.J. Ablowitz, R. Halburd, and B. Herbst, On the extension of the Painlev´e property to difference equations. Nonlinearity 13 (2000), pp. 889-905. [OpenAIRE]

19 references, page 1 of 2