Construction of Multidimensional Vector Fields Whose Projections Onto Coordinate Planes Have Given Topological Structures

The aim of the work is to construct multidimensional vector fields that are represented by autonomous systems of ordinary differential equations and have specified topological structures in specified limited simply connected domains of the phase space provided that these structures can be specified by topological structures of projections of the sought vector fields onto coordinate planes. This problem is an inverse problem of the qualitative theory of ordinary differential equations. The results of this work can be used to construct mathematical models of dynamic systems in various fields of science and technology. In particular, for mechanical systems with an arbitrary finite number of degrees of freedom, such vector fields can represent kinematic equations of program motions and be used to obtain control forces and moments implementing these motions. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.