title: Chaos and Integrability in Nonlinear Dynamics: An Introduction
author:  Michael Tabor 
description: Presents the newer field of chaos in nonlinear dynamics as a natural extension of classical mechanics as treated by differential equations. Employs Hamiltonian systems as the link between classical and nonlinear dynamics, emphasizing the concept of integrability. Also discusses nonintegrable dynamics, the fundamental KAM theorem, integrable partial differential equations, and soliton dynamics.
zlib_text: Chapter 12
  Robust Chaos in 2-D
  Piecewise-Smooth Maps
  In this chapter, we discuss robust chaos in two-dimensional piecewise-
  smooth maps. In Sec. 12.1.1, we give the normal form of these maps to
  facilitate the study of bifurcations and chaos. Section 12.1.2 provides details
  about bifurcations and chaos obtained using such a normal form, including
  general classiﬁcations and diﬀerent routes to chaos. Section 12.1.3 deals
  with regions in the parameter space of the normal form with nonrobust
  chaos, and Sec. 12.1.4 describes regions for robust chaos. In Sec. 12.1.5, we
  give a proof of unicity of the orbits for the normal form, and in Sec. 12.1.6 a
  proof of the robustness of chaos in two-dimensional piecewise-smooth maps
  is given along with two examples. In Sec. 12.2, the same strategy as above
  is applied to the two-dimensional noninvertible piecewise-linear maps with
  their normal form as given in Sec. 12.2.1, and a proof of robust chaos is
  given in Sec. 12.2.2 with some examples. In Sec. 12.