5 papers
Higher-order and non-geometric symmetries and Noether's theorem in k-cosymplectic Hamiltonian field theory
Manuel de León, Xuefeng Zhao
In this paper, we investigate higher-order symmetries and non-geometric symmetries within the framework of -cosymplectic Hamiltonian field theory. We introduce the concept of ge…
Integrability of Hamiltonian systems on COLCS Manifold
Antonio J. Pan-Collantes, Xuefeng Zhao
We develop an integrability framework for Hamiltonian dynamics on \emph{con-locally conformal symplectic} (COLCS) manifolds, odd-dimensional quadruples where $dΩ=θ\wedg…
A geometric approach to the (generalized) Noether theorem for Hamiltonian systems on (non)-uniform q-contact manifolds
Manuel de León, Cristina Sardón, Xuefeng Zhao
In this paper, we develop a unified Hamiltonian framework for dynamical systems with multiple independent dissipation channels based on q-contact geometry. As an application, we em…
Noether-Type Theorems and the Generalized Herglotz Principle in -Contact Geometry
Melvin Leok, Cristina Sardón, Xuefeng Zhao
We develop a unified geometric framework for dissipative mechanical systems based on uniform -contact manifolds, which provide an extended phase space equipped with multiple con…
Canonical and Canonoid transformations for Hamiltonian systems on locally conformal symplectic manifolds
Rafael Azuaje, Xuefeng Zhao
This paper is focused on the development of the notions of canonical and canonoid transformations within the framework of Hamiltonian Mechanics on locally conformal symplectic mani…