Example of robust chaos in a smooth map

Abstract

Robust chaos is defined by the absence of periodic windows and coexistingattractors in some neighborhood of the parameter space. The occurrence of robustchaos has been discussed in Phys. Rev. Lett., 78 (1997) 4561 and Phys.Rev. Lett., 80 (1998) 3049. It has been shown that robust chaos can occurin piecewise smooth systems. Also, it has been conjectured that robust chaoscannot occur in smooth systems. However, here we give a counterexample to thisconjecture. We present a one-dimensional smooth map xt + 1 = f(xt,α)that generates robust chaos in a large domain of the parameter space (α).