By Valerij V. Kozlov
John Hornstein has written in regards to the author's theorem on nonintegrability of geodesic flows on closed surfaces of genus more than one: "Here is an instance of ways differential geometry, differential and algebraic topology, and Newton's legislation make track jointly" (Amer. Math. Monthly, November 1989).
Kozlov's e-book is a scientific creation to the matter of actual integration of equations of dynamics. the foremost to the answer is to discover nontrivial symmetries of Hamiltonian platforms. After Poincaré's paintings it turned transparent that topological concerns and the research of resonance phenomena play an important position within the challenge at the life of symmetry fields and nontrivial conservation laws.