Point-to-periodic and periodic-to-periodic connections
The authors consider computing and continuing connecting orbits in parameter dependent dynamical systems. Some details of algorithms for computing connections between equilibria and periodic orbits, and between periodic orbits are given. The theoretical foundation of these techniques is given in the seminal work of \textit{W.-J. Beyn} [Contemp. Math. 172, 131--168 (1994; Zbl 0813.58046)], where a numerical technique is proposed. The algorithms consist of splitting the computation of the connection from that of the periodic orbit(s). To set up appropriate boundary conditions, the authors follow the algorithmic approach used by \textit{J. W. Demmel, L. Dieci} and {M. J. Friedman} [SIAM J. Sci. Comput. 22, No. 1, 81--94 (2000; Zbl 0967.34008)], for the case of connecting orbits between equilibira, and construct and exploit the smooth block Schur decomposition of the monodromy matrices associated to the periodic orbits. Numerical examples illustrate the performance of the algorithms. Finally, it should be mentioned that the paper contains many misprints that invalid some technical results so that a complete revision would be desirable.
scientific article; zbMATH DE number 2081528