BIFURCATIONS AND ROTATION NUMBERS FOR MAPS OF THE CIRCLE ASSOCIATED WITH FLOWS ON THE TORUS AND MODELS OF CARDIAC-ARRHYTHMIAS

Degree-one maps of the circle which are monotonic but have a single po int of discontinuity and a single plateau arise naturally in a variety of contexts. Properties of rotation numbers associated with such maps are investigated, and in particular the dependence of the rotation nu mber on the value assigned to the map at the point of discontinuity is discussed. The unfolding of a codimension-two bifurcation is also des cribed.