Piecewise smooth maps occur in a variety of physical systems. We show that in a two-dimensional continuous map a chaotic orbit can exist even when the map is contractive (eigenvalues less than unity in magnitude) at every point in the phase space. In this Letter we explain this peculiar feature of piecewise smooth continuous maps.
Dr. Biswambhar Rakshit and Banerjee, S., “Existence of chaos in a piecewise smooth two-dimensional contractive map”, Physics Letters A, vol. 373, pp. 2922 - 2926, 2009.