Properties of infinite dimensional Hamiltonian systems
To appreciate these notes the reader should be well grounded in the theory of finite-dimensional Hamiltonian and Lagrangian systems, symplectic manifolds, and Lie groups. The purpose of these notes is to generalize all of this material to infinite dimensions, where the difference between the bounded und unbounded linear operators becomes important. In this regard the authors lean heavily on such tools as Stone's theorem and the Hille-Yosida theorem. Many examples from quantum mechanics and symmetric hyperbolic systems of partial differential equations are given by the authors to show the applicability of this approach. Contents: Ch. 1: Symplectic structures and Hamiltonian systems. Ch. 2: Linear Hamiltonian systems. Ch. 3: Some general properties of nonlinear semigroups. Ch. 4: Hamiltonian systems. Ch. 5: Lagrangian systems. Ch. 6: Symmetry groups and conservation laws.
infinite dimensional Hamiltonian systems
scientific article; zbMATH DE number 3471338