Generic Hamiltonian Dynamical Systems are Neither Integrable nor ErgodicAmerican Mathematical Soc., 1974 - 52 pages This memoir gives an introduction to Hamiltonian dynamical systems on symplectic manifolds, including definitions of Hamiltonian vector fields, Poisson brackets, integrals of motion, complete integrability, and ergodicity. A particularly complete treatment of action-angle coordinates is given. Historical background into the question of ergodicity and integrability in Hamiltonian systems is also given. |
Table des matières
| 1 | |
2 Global Hamiltonian Dynamics on Symplectic Manifolds | 5 |
3 ActionAngle Coordinates and Integrability | 17 |
4 Elliptic Equilibria and Ergodicity | 33 |
5 Superintegrability and Some Remarks on Noncompact Manifolds | 47 |
| 51 | |
Autres éditions - Tout afficher
Generic Hamiltonian Dynamical Systems are Neither Integrable Nor Ergodic Lawrence Markus,Kenneth Ray Meyer Aucun aperçu disponible - 1974 |
Generic Hamiltonian Dynamical Systems are Neither Integrable nor Ergodic Lawrence Markus,Kenneth Ray Meyer Aucun aperçu disponible - 1974 |
Expressions et termes fréquents
2n-manifold action-angle coordinates action-angle variables analytic Hamiltonian B₂ Baire space C-topology canonical coordinates classical mechanics commuting compact manifold compact symplectic manifold completely integrable corresponding cotangent bundle countable defined dense in H dense set diffeomorphism dynamical system eigenvalues elliptic critical point energy manifold flow dH function H g is dense H₁ H₂ Hamiltonian differential Hamiltonian dynamics Hamiltonian flow Hamiltonian function Hamiltonian matrix Hamiltonian system Hamiltonian vector fields Hence integrable Hamiltonians integral curve invariant tori LEMMA level H linear space main theorem meager in H metric minimal n-tori neighborhood noncompact symplectic manifolds nondegenerate action-angle nonempty open set nonergodic nonsingular normalized Hamiltonians open and dense open interval open set P₁ Poisson bracket real analytic real differentiable function regular and consists regular value rotation numbers space H submanifold symplectic manifold M²n T*M¹ tangent space topology torus vector fields dF θα