Lecture 16: Orbits in axisymmetric potentials
Binney and Tremaine, 3.2
The following are the standard texts on modern classical mechanics:
Lichtenberg, A. J., and Lieberman, M. A. 1992, Regular and chaotic dynamics (New York: Springer) - chaos and nonlinear dynamics, including surfaces of section. Not all that well written, but fairly complete
Arnold, V. I. 1974, Mathematical Methods of Classical Mechanics (New York: Springer) - an elegant but spare treatment of Hamiltonian dynamics; possibly too mathematical for most physicist's tast
Sussman, G. I., and Wisdom, J. 2001, Structure and Interpretation of Classical Mechanics (Cambridge: MIT Press) - somewhat idiosyncratic and user-unfriendly, but an original and deep treatment of modern mechanics
Jose, J. V., and Saletan, E. J. 1999, Classical Mechanics: A Contemporary Approach (Cambridge: Cambridge University Press)
The classic texts are Goldstein and Landau and Lifshitz. Bothe give excellent treatments of classical mechanics but ignore almost all of the developments of the last century.
Henon, M., and Heiles, C. 1964, AJ 69, 73 - one of the classic papers in nonlinear dynamics. Also treated in Lichtenberg & Lieberman.