  Sergey Pinchuk discovered a class of pairs of real polynomials in two
variables that have a nowhere vanishing Jacobian determinant and define maps of
the real plane to itself that are not one-to-one. This paper describes the
asymptotic behavior of one specific map in that class. The level of detail
presented permits a good geometric visualization of the map. Errors in an
earlier description of the image of the map are corrected (the complement of
the image consists of two, not four, points). Techniques due to Ronen Peretz
are used to verify the description of the asymptotic variety of the map.
