Notes on Dynamical Systems Book

Ch. 1	Transformation theory	1
	Differential equations and vector fields	1
	Variational principles, Hamiltonian systems	11
	Canonical transformations	19
	Hamilton-Jacobi equations	29
	Integrals and group actions	41
	The SO(4) symmetry of the Kepler problem	52
	Symplectic manifolds	62
	Hamiltonian vector fields on symplectic manifolds	73
Ch. 2	Periodic orbits	85
	Poincare's perturbation theory of periodic orbits	85
	A theorem by Lyapunov	94
	A theorem by E. Hopf	98
	The restricted 3-body problem	102
	Reversible systems	108
	The plane 3- and 4-body problems	116
	Poincare-Birkhoff fixed point theorem	120
	Variations on the fixed point theorems	133
	The billiard ball problem	140
	A theorem by Jacobowitz and Hartman	149
	Closed geodesics on a Riemannian manifold	160
	Periodic orbits on a convex energy surface	172
	Periodic orbits having prescribed periods	181
Ch. 3	Integrable Hamiltonian systems	187
	A theorem of Arnold and Jost	187
	Delaunay variables	199
	Integrals via asymptotics; the Stormer problem	207
	The Toda lattice	213
	Separation of variables	228
	Constrained vector fields	234
	Isospectral deformations	242