The Continuous Diophantine Approximation Mapping of Szekeres

Szekeres defined a continuous analogue of the additive ordinary continued fraction expansion, which iterates a map T on a domain which can by identified with the unit square [0,1]sup 2. Associated to it are continuous analogues of the Lagrange and Markoff spectrum. Out main result is that these are identical with the usual Lagrange and Markoff spectra, respectively, thus providing an alternative characterization of them.