Mappings Associated with Classical Conformal of the Second Kind in $\mathbf R^3$ and Problems of Stationary Meridional Velocity Fields in Inhomogeneous Media

During ICNAAM 2011–2014 the author demonstrated some properties of axially symmetric generalizations of conformal mappings of the second kind in the framework of Fueter construction in $\mathbf R^3$. Corresponding models of stationary meridional velocity fields in an axially symmetric inhomogeneous medium were characterized in terms of gradient dynamical systems. New quadratic and cubic gradient dynamical systems with variable dissipation were described.
However, geometric properties of singular sets of axially symmetric generalizations of conformal mappings of the second kind have been insufficiently studied. Hypothesis about properties of the Jacobian matrix in the framework of Fueter's construction, formulated by the author during ICNAAM 2014, was proved by the author jointly with U. Kähler (Aveiro, Portugal) in 2015. In particular, problems of singular sets of an axially symmetric generalization of Joukowski transformation in $\mathbf R^3$ are discussed now.