Examples of nonintegrable Hamiltonians in real analytic mechanics
Using the meromorphic nonintegrability theorems of \textit{S. L. Ziglin} [Funct. Anal. Appl. 16, 181--189 (1983; Zbl 0524.58015) and ibid. 17, 6--17 (1983; Zbl 0518.58016)] and \textit{J. Morales-Ruiz} and \textit{J. P. Ramis} [Methods Appl. Anal. 8, 33--95 (2001; Zbl 1140.37352) and ibid. 8, 97--111 (2001; Zbl 1140.37354)] several examples of real nonintegrable Hamiltonian systems on (open subsets of) \(\mathbb R^4\) are presented. Among them, there are two remarkable, namely Hénon-Heiles and Yang-Mills with the gauge group \(SU(2)\).
scientific article; zbMATH DE number 2074285