Abstract
In this paper, we derive the invariants for discriminating the existence of nesting in the shape of the divergence-convergence boundary of two-dimensional real homogeneous quadratic transformations. Nesting in this context is a special case of self-similarity in the general sense. To explain the properties of this shape, we analyze nesting in the portrait of the behavior of directions in the transformation process. For two-dimensional real homogeneous guadratic transformations, Date and Iri [1] gave the invariant series. We found an additional invariant for discriminating the nesting.
