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Heuristic definitions of terms.

• .dat the suffix for a file containing all the data to specify one of the manifold objects (the data is readable by the manifold objects).
• .vect the suffix for a file containing data for displaying a picture of one of the manifold objects (the data is readable by Geomview).
• boundary element an element in an approximation to a manifold which is near the boundary of the ambient space, if there is a boundary.
• continue/continuation the process of repeatedly increasing/decreasing a parameter of a dynamical system and locating an invariant manifold of the "new" system as a perturbation of the invariant manifold for the "old" system.
• current manifold the known manifold obtained from the last graph transform iterate.
• grid points the points in ambient space used to approximate a manifold embedded in ambient space. For example, the vertices of a simplicial complex.
• manifold object an object of a class designed to represent a manifold, that is, a "d1baseMan", "d1graphMan", "d2LTManifold", "d2graphMan", "manifold_hyp", or "graphMan_hyp".
• nodes the points of a (1 or 2 dimensional) simplex corresponding to the principal lattice of order p, where p is the order of the approximation.
• normal fiber an affine subspace embedded in ambient space which is complementary and nearly orthogonal to the tangent space of a manifold.
• next manifold the unknown manifold being solved for by the current iterate of the graph transform algorithm. A point on this manifold is obtained in the normal fiber at each grid point.
• search data data which "tells" the graph transform algorithm approximately what part of the current manifold is mapped (by the dynamical system) "above" the grid point being solved. Without this data, the algorithm is much slower.
• truncated coordinates the standard coordinates on the ambient space which represent values on the circle, as opposed to values on the real line. For example, if the ambient space is a cylinder R^{1}xS^{1}, the second coordinate (on S^{1}) is called a truncated coordinate.
• zeroing a graphman setting the grid points of an object of class d2graphMan, d1graphMan, or graphMan_hyp so that the manifold represented by these objects corresponds to the initial manifold.

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