INTEGRABLE LATTICE MAPS: QV, A RATIONAL VERSION OF Q4
Glasgow mathematical journal, Tome 51 (2009) no. A, pp. 157-163

Voir la notice de l'article provenant de la source Cambridge University Press

We describe a family of integrable lattice maps related to the known quad maps Q4. The integrability criterion we use is the vanishing of the algebraic entropy. The family has the advantage of being parametrized rationally: all its parameters are unconstrained.
DOI : 10.1017/S0017089508004874
Mots-clés : 37K10, 52C99, 39A10
VIALLET, CLAUDE M. INTEGRABLE LATTICE MAPS: QV, A RATIONAL VERSION OF Q4. Glasgow mathematical journal, Tome 51 (2009) no. A, pp. 157-163. doi: 10.1017/S0017089508004874
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[1] 1.Adler, V. E., Bäcklund transformation for the Krichever–Novikov equation, Int. Math. Res. Notices 1 (1998), 1–4. arXiv:solv-int/9707015. Google Scholar | DOI

[2] 2.Adler, V. E., Bobenko, A. I. and Suris, Y. B., Classification of integrable equations on quad-graphs. The consistency approach. Comm. Math. Phys. 233 (3) (2003), 513–543. arXiv:nlin.SI/0202024. Google Scholar | DOI

[3] 3.Adler, V. E., Bobenko, A. I. and Suris, Y. B., Discrete nonlinear hyperbolic equations. Classification of integrable cases, Funct. Anal. Appl. (to appear). arXiv:0705.1663. Google Scholar

[4] 4.Adler, V. E. and Suris, Y. B., Q : Integrable master equation related to an elliptic curve, Int. Math. Res. Notices 47 (2004), 2523–2553. arXiv:nlin.SI/0309030. Google Scholar

[5] 5.Bellon, M. and Viallet, C-M., Algebraic Entropy, Comm. Math. Phys. 204 (1999), 425–437. chao-dyn/9805006. Google Scholar | DOI

[6] 6.Bobenko, A. I. and Suris, Y. B., Integrable systems on quad-graphs, Int. Math. Res. Notices 11 (2002), 573–611. arXiv:nlin/0110004v1 [nlin.SI]. Google Scholar | DOI

[7] 7.Drinfeld, V. G.. On some unsolved problems in quantum group theory. In Quantum groups, volume 1510 of Lecture Notes in Math, pp. 1–8 (Springer, Berlin, 1992). Google Scholar

[8] 8.Falqui, G. and Viallet, C.-M., Singularity, complexity, and quasi–integrability of rational mappings, Comm. Math. Phys. 154 (1993), 111–125. hep-th/9212105. Google Scholar | DOI

[9] 9.Hietarinta, J., Searching for CAC-maps, J. Nonlinear Math. Phys. 12 (2005), 223–230. Google Scholar | DOI

[10] 10.Hietarinta, J. and Viallet, C.-M.. On the parametrization of solutions of the Yang–Baxter equations. (q-alg/9504028) (1995). Available from . Google Scholar | arXiv

[11] 11.Hietarinta, J. and Viallet, C.-M., Singularity confinement and chaos in discrete systems, Phys. Rev. Lett. 81 (2) (1998), 325–328. solv-int/9711014. Google Scholar | DOI

[12] 12.Hietarinta, J. and Viallet, C-M., Searching for integrable lattice maps using factorization. P. Phys. A 40 (2007), 12629–12643. arXiv:0705.1903. Google Scholar

[13] 13.Nijhoff, F., Lax pair for the Adler (lattice Krichever–Novikov) system, Phys. Lett. A 297 (2002), 49–58. arXiv:nlin.SI/0110027. Google Scholar | DOI

[14] 14.Tongas, A. G.Papageorgiou, V. G., Yang–Baxter maps and multi-field integrable lattice equations, J. Phys. A 40 (2007), 12677–12690. arXiv:math/0702577. Google Scholar

[15] 15.Tremblay, S., Grammaticos, B. and Ramani, A., Integrable lattice equations and their growth properties. Phys. Lett. A 278 (2001), 319–324. Google Scholar | DOI

[16] 16.Veselov, A. P., Yang–Baxter maps and integrable dynamics, Phys. Lett. A 314 (2003), 214–221. Google Scholar | DOI

[17] 17.Viallet, C-M.. Algebraic entropy for lattice equations. Available from . Google Scholar | arXiv

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