ABSTRACT
This chapter considers in detail the Henon map, the linearly coupled logistic map and the conservative twist map, and looks at the complex logistic map. It also looks into some of the more general aspects of higher dimensional maps. The full unstable manifold may be thought of as the space generated by an infinity of iterations of all points within some infinitesimal volume element spanned by all eigenvectors corresponding to eigenvectors of the Jacobian matrix of absolute value greater than one. The chapter demonstrates that the Lyapunov exponent is a very useful means to explore the general structures occurring in phase space as a function of the parameter of the logistic map. To calculate the Hausdorff dimension on a computer, or more commonly the capacity, is even more time and much more memory consuming than to calculate the Lyapunov exponents.
