Year: 2025
Type: article
Abstract: Dynamical systems more general than Hamiltonian systems are considered. The role of the Hamiltonian function is played by a 1-form (not necessarily closed) on a symplectic phase space. A bracket of such forms is introduced and a generalized Liouville theorem on the complete integrability is formulated. This generalization allows us to better understand the meaning of the conditions of the classical theorem on the complete integrability of the Hamilton equations and to reveal the role of tensor invariants.
Author: Valery Kozlov
Institution: Steklov Mathematical Institute
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4411252027