Zeng, Yunbo; Li, Yishen New symplectic maps: integrability and Lax representation. (English) Zbl 0890.58018 Chin. Ann. Math., Ser. B 18, No. 4, 457-466 (1997). Summary: A new family of integrable symplectic maps is reduced from the Toda hierarchy via constraint for a higher flow of the hierarchy in terms of square eigenfunctions. Their integrability and Lax representation are deduced systematically from the discrete zero-curvature representation of the Toda hierarchy. Also a discrete zero-curvature representation for the Toda hierarchy with sources is presented. Cited in 6 Documents MSC: 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) Keywords:higher-order constraints; integrable symplectic maps; Lax representation; discrete zero-curvature representation PDFBibTeX XMLCite \textit{Y. Zeng} and \textit{Y. Li}, Chin. Ann. Math., Ser. B 18, No. 4, 457--466 (1997; Zbl 0890.58018)