Querying databases of trajectories of differential equations. I. Data structures for trajectories

One approach to qualitative reasoning about dynamical systems is to extract qualitative information by searching or making queries on databases containing many trajectories. The efficiency of such queries depends crucially upon finding an appropriate data structure for trajectories of dynamical systems. Suppose that a large number of parameterized trajectories γ of a dynamical system evolving in R ^N are stored in a database. Let η⊂R^N denote a parameterized path in Euclidean space. A data structure is defined to represent trajectories of dynamical systems, and a sketch is given of an algorithm which answers queries of the following form: Query: return the trajectory γ from the database which minimizes the norm on the space of paths ||η-γ||