Topological equivalence of local singularities of a particular type for dynamical systems with shock interactions. (Q1566450)

The author continues the study of local singularities of dynamical systems with shock interactions. In particular, the attention is restricted to the singularities of the sixth type (according to the classification introduced by the author [Mat. Zametki 64, 531--542 (1998; Zbl 0926.34031)]), that is, to the points on the shock hypersurface \(S=0\) characterized by the conditions \[ x_{n}=0,\quad\dot{x}_{n}=0,\quad\ddot{x}_{n}=0,\quad x_{n}^{\prime\prime \prime}<0. \] For two systems with local singularities of the sixth type, the main result establishes the existence of sufficiently small neighborhoods of singularities in the phase spaces of the corresponding systems with identical topological structure.