Stable topological non-conjugacy of Hamiltonian systems on two-dimensional surfaces
The regular Morse functions are studied on two-dimensional surfaces. These functions possess the property of stability in the following sense. Two Hamiltonian systems are stable topologically non-conjugated near the saddle critical levels, if (1) these Hamiltonian systems are not topologically conjugated in any arbitrary small neighborhoods \(U_1\) and \(U_2\) of saddle levels; (2) for any arbitrary small perturbations of the functions \(F_1\) and \(F_2\) and the si mplectic structures \(\omega_1\) and \(\omega_2\) the perturbed systems remain topologically non-conjugated in any domains \(\tilde U_1\) and \(\tilde U_2\) containing \(U_1\) and \(U_2\) respectively. The authors describe the natural subclass in the set of all such Morse functions.
scientific article; zbMATH DE number 1524038