Symmetries, Topology and Resonances in Hamiltonian Mechanics

John Hornstein has written about the author's theorem on nonintegrability of geodesic flows on closed surfaces of genus greater than one: "Here is an example of how differential geometry, differential and algebraic topology, and Newton's laws make music together" ( Amer. Math. Monthly , November 1989). Kozlov's book is a systematic introduction to the problem of exact integration of equations of dynamics. The key to the solution is to find nontrivial symmetries of Hamiltonian systems. After Poin