A lower estimate of the codimension of the set of Fuller points (Q1776280)

The author considers the following Hamiltonian system \[ \dot{\psi} = -\frac{\partial H}{\partial x},\;\;\dot{x} = \frac{\partial H}{\partial \psi},\tag{1} \] where \(\psi\in \mathbb{R}^{n}, x\in \mathbb{R}^{n}, H = H_{0}(\psi,x) + u H_{1}(\psi, x)\), and \(u = sgn H_{1}(\psi,x)\), \(H_{0}\), \(H_{1}\) being functions of class \(C^{\infty}\) in their variables. It is studied Eq(1) locally, in a small neighborhood of some point \((\psi_{0}, x_{0})\) such that \(H_{1}(\psi_{0}, x_{0})=0\) and grad \(H_{1}(\psi_{0}, x_{0})\neq 0.\) In the paper the research is carried out on Hamiltonian systems with a tangential discontinuity for generic points in the codimension 4. The main result is that there are no Fuller points among generic singular points of codimension 4. Thus, the lower estimate of the set of Fuller points is at least greater or equal to 5.