ABSTRACT
This chapter is devoted to presenting some results of the rigorous determination of the Lyapunov exponents of some 2-D discrete mappings. In Sec. 5.1, the Lyapunov exponents of the discrete hyperchaotic double scroll mapping are calculated and the bifurcation parameters, in which the result attractor is hyperchaotic, are estimated. In Sec. 5.2, the Lyapunov exponents of a class of 2-D piecewise linear mappings are calculated; this case includes the so-called “discrete butterfly”. In Sec. 5.3, the Lyapunov exponents of a family of 2-D discrete mappings with separate variables are presented under some comparable conditions on the functions defining the system. Finally, the Lyapunov exponents of a discontinuous piecewise linear mapping of the plane governed by a simple switching law are calculated and discussed in Sec. 5.4. Some interesting dynamical phenomena are also present for an elementary example.
