Symmetries, Topology and Resonances in Hamiltonian Mechanics [Paperback]

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 Poincar?'s work it became clear that topological considerations and the analysis of resonance phenomena play a crucial role in the problem on the existence of symmetry fields and nontrivial conservation laws.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 Poincar?'s work it became clear that topological considerations and the analysis of resonance phenomena play a crucial role in the problem on the existence of symmetry fields and nontrivial conservation laws.I Hamiltonian Mechanics.- 1 The Hamilton Equations.- 2 Euler-Poincar? Equations on Lie Algebras.- 3 The Motion of a Rigid Body.- 4 Pendulum Oscillations.- 5 Some Problems of Celestial Mechanics.- 6 Systems of Interacting Particles.- 7 Non-holonomic Systems.- 8 Some Problems of Mathematical Physics.- 9 The Problem of Identification of Hamiltonian Systems.- II Integration of Hamiltonian Systems.- 1 Integrals. Classes of Integrals of Hamiltonian Systems.- 2 Invariant Relations.- 3 Symmetry Groups.- 4 Complete Integrability.- 5 Examplesl³¬