9 papers
Duality of Hamiltonian and Lagrangian formulations for integrable systems
Pierandrea Vergallo, Mats Vermeeren
We introduce the concept of Hamiltonian potential variables to map Hamiltonian operators into symplectic operators in a dual space. This generalises the classical trick of switchin…
Lagrangian multiforms and dispersionless integrable systems
Evgeny V. Ferapontov, Mats Vermeeren
We demonstrate that interesting examples of Lagrangian multiforms appear naturally in the theory of multidimensional dispersionless integrable systems as (a) higher-order conservat…
Discrete Lagrangian Multiforms for ABS Equations I: Quad Equations
Jacob J. Richardson, Mats Vermeeren
Discrete Lagrangian multiform theory is a variational perspective on lattice equations that are integrable in the sense of multidimensional consistency. The Lagrangian multiforms f…
Discrete Lagrangian Multiforms for ABS Equations II: Tetrahedron and Octahedron Equations
Jacob J. Richardson, Mats Vermeeren
We present four types of discrete Lagrangian 2-form associated to the integrable quad equations of the ABS list. These include the triangle Lagrangian that has traditionally been u…
Structure preserving discretization of time-reparametrized Hamiltonian systems with application to nonholonomic mechanics
Luis C. García-Naranjo, Mats Vermeeren
We propose a discretization of vector fields that are Hamiltonian up to multiplication by a positive function on the phase space that may be interpreted as a time reparametrization…
Numerical integration in celestial mechanics: a case for contact geometry
Alessandro Bravetti, Marcello Seri, Mats Vermeeren +1
Several dynamical systems of interest in celestial mechanics can be written in the form of a Newton equation with time-dependent damping, linear in the velocities. For instance, th…