Identifying linear vector fields on 2D manifolds

Abstract

Local linearity of vector fields is a property that is well researched and understood. Linear approximation can be used to simplify algorithms or for data reduction. Whereas the concept is easy to implement in 2D and 3D, it loses meaning on manifolds as linearity has either to be defined based on an embedding in a higher-dimensional Cartesian space or on a map. We present an adaptive atlas-based vector field decomposition to solve the problem on manifolds and present its application on synthetic and climate data.