Covering relations for multidimensional dynamical systems. II
This article is based on part I [J. Differ. Equations 202, No.~1, 32--58 (2004; Zbl 1061.37013)] by the same authors. Using a topological approach, the authors prove the existence of chaotic orbits in certain Hamiltonian systems with several degrees of freedom. A topological crossing condition for tori replaces the usual transversality and using covering relations, it is shown that arbitrary itineraries to such tori can be realized. The work is based on ideas by \textit{R. W. Easton} [J. Differ. Equations 29, 241--252 (1978; Zbl 0392.58003) and Classical mechanics and dynamical systems, NSF-CBMS reg. Conf., Tufts Univ. 1979, Lect. Notes Pure Appl. Math. 70, 55--67 (1981; Zbl 0502.70024)].
scientific article; zbMATH DE number 2092984
scientific article