Geodesic Holonomy Attractor between Surfaces of Different Curvature Signs relevant to Spin Transport

We will consider nonlinear holonomy effects -especially the spin dissipation dynamicsarising in the transport of a linear rotator between metric spaces with different curvature (positive, zero, negative). The extra 3D spin vector current induced by curvature or metric distortion provides for a holonomic attractor called ”Magic Angle Precession” (MAP). Limitations and instabilities of the spin current exchange are assigned to bifurcations at high precession loads as the driving gauge potential. In the classical range the chaotic dynamics can be verified with a mechanical toy gyroscope with built-in spin-precession coupling that could also be modeled by a Chua-type electronic circuit. Transporting vector currents composed by spin and precession is treated by Schwarz-Christoffel triangle conformal maps with constant Schwarzian derivative and hypergeometric monodromy. Handling both curvatures simultaneously as a metric distortion is possible by a composite hypergeometric mapping function linearly composed as a ladder/recurrence relation between dual hypergeometric functions related by inversion. This leads to the well known Schrödinger hypergeometric quantum mechanical solution providing for Pöschl-Teller type potentials, quantization, factorization, and ladder operators. By pull-back we get the generalized Gauss linking number density differential form.