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 ...