Computer Geometry and Topological Classification of Integrable Hamiltonian Differential Equations: Visualization of Concrete Physical Examples

Abstract

The work contains new results in computer geometry, Hamiltonian mechanics and simplectic topology. Topological classification of integrable Hamiltonian dynamical systems with two degrees of freedom. Visualization of the evolution of the solutions for integrable systems. Computer experiments, real physical integrable systems and their place in the Table of all “mathematically existing” integrable Hamiltonian systems. There exists the algorithm of recognition of topologically equivalent (and topologically non-equivalent) systems.