INFINITE NUMBER OF PARAMETER REGIONS WITH FRACTAL NONCHAOTIC ATTRACTORS IN A PIECEWISE MAP

We identify a countable infinity of parameter regimes with strange nonchaotic attractors (SNAs). At the edge of each arc parameter area, there is an uncountable infinity of SNAs with torus intermittency. The mechanism for the creation of SNAs in different regime is induced by an [Formula: see text]-frequency quasiperiodic orbit through a quasiperiodic analog of saddle-node bifurcation (Type-[Formula: see text] intermittent route). We describe the transition between tori and SNAs by the largest Lyapunov exponent and phase diagram. These SNAs are characterized by the phase sensitivity exponents, rational approximations, singular-continuous spectra, and distribution of finite-time Lyapunov exponents.