We extend the investigation of three-dimensional Hamiltonian systems of non-subgroup type admitting non-zero magnetic fields and an axial symmetry, namely the circular parabolic case, the oblate spheroidal case and the prolate spheroidal case. More precisely, we focus on linear and some special cases of quadratic superintegrability. In the linear case, no new superintegrable system arises. In the quadratic case, we found one new minimally superintegrable system that lies at the intersection of the circular parabolic and cylindrical cases and another one at the intersection of the cylindrical, spherical, oblate spheroidal and prolate spheroidal cases. By imposing additional conditions on these systems, we found for each quadratically minimally superintegrable system a new infinite family of higher-order maximally superintegrable systems. These two systems are linked respectively with the caged and harmonic oscillators without magnetic fields through a time-dependent canonical transformation.

我们扩展了非子类型的三维哈密顿系统的研究，该系统允许非零磁场和轴向对称性，即圆形抛物线形，扁球形和扁球形。更准确地说，我们专注于线性和二次超可积性的一些特殊情况。在线性情况下，不会出现新的超积分系统。在二次情况下，我们发现了一个新的最小超可积系统，该系统位于圆形抛物线和圆柱壳的交点处，另一个位于圆柱，球面，扁球体和扁球体的交点处。通过在这些系统上施加附加条件，我们为每个二次最小可超积分系统找到了一个新的无穷高阶最大可超积分系统。