sentences:  Often the original mapping formula_6 is from a Banach space into itself, and the Euclidean n-space is a finite-dimensional approximation to the Banach space.A steady state, or fixed point, of a parameterized family of flows or maps are of this form, and by discretizing trajectories of a flow or iterating a map, periodic orbits and heteroclinic orbits can also be posed as a solution of formula_7.In some nonlinear systems, parameters are explicit.