相关论文: The optimal momentum map

In this paper we proposed a proposition: for any nonconservative classical mechanical system and any initial condition, there exists a conservative one; the two systems share one and only one common phase curve; the Hamiltonian of the…

Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulations. Geometric integrators are widely used for this purpose,…

We discuss the relation between symmetries and conservation laws in the realm of classical field theories based on the Hamiltonian constraint. In this approach, spacetime positions and field values are treated on equal footing, and a…

We consider symmetries and perturbed symmetries of canonical Hamiltonian equations of motion. Specifically we consider the case in which the Hamiltonian equations exhibit a Lambda symmetry under some Lie point vector field. After a brief…

Classical Hamiltonian mechanics, characterized by a single conserved Hamiltonian (energy) and symplectic geometry, `hides' other invariants into symmetries of the Hamiltonian or into the kernel of the Poisson tensor. Nambu mechanics aims to…

In this paper we study the reduction of a nonholonomic system by a group of symmetries in two steps. Using the so-called 'vertical-symmetry' condition, we first perform a 'compression' of the nonholonomic system leading to an almost…

This work presents a general geometric framework for simulating and learning the dynamics of Hamiltonian systems that are invariant under a Lie group of transformations. This means that a group of symmetries is known to act on the system…

An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework…

It's well known that Noether symmetries lead to the conservation laws. Conserved quantities are constructed out of generator of the symmetry - invariant Hamiltonian vector field. Considering more general class of vector fields -…

Gyrokinetic field theory is addressed in the context of a general Hamiltonian. The background magnetic geometry is static and axisymmetric, and all dependence of the Lagrangian upon dynamical variables is in the Hamiltonian or in free field…

Many numerical and learning algorithms rely on the solution of the Monge-Kantorovich problem and Wasserstein distances, which provide appropriate distributional metrics. While the natural approach is to treat the problem as an…

We study diffeomorphisms that have one-parameter families of continuous symmetries. For general maps, in contrast to the symplectic case, existence of a symmetry no longer implies existence of an invariant. Conversely, a map with an…

One main issue, when numerically integrating autonomous Hamiltonian systems, is the long-term conservation of some of its invariants, among which the Hamiltonian function itself. For example, it is well known that classical symplectic…

After a brief survey of the definition and the properties of Lambda-symmetries in the general context of dynamical systems, the notion of "Lambda-constant of motion'' for Hamiltonian equations is introduced. If the Hamiltonian problem is…

This paper develops the reduction theory of implicit Hamiltonian systems admitting a symmetry group at a singular value of the momentum map. The results naturally extend those known for (explicit) Hamiltonian systems described by Poisson…

In this paper we will present Lagrangian and Hamiltonian $k$-symplectic formalisms, we will recall the notions of symmetry and conservation law and we will define the notion of pseudosymmetry as a natural extension of symmetry. Using…

We review in detail the Hamiltonian dynamics for constrained systems. Emphasis is put on the total Hamiltonian system rather than on the extended Hamiltonian system. We provide a systematic analysis of (global and local) symmetries in total…

Over the past two decades, open systems that are described by a non-Hermitian Hamiltonian have become a subject of intense research. These systems encompass classical wave systems with balanced gain and loss, semiclassical models with mode…

In this work, a nonlinear momentum method is introduced to enhance the convergence performance of momentum-based gradient optimization algorithms. Classical momentum methods, such as the Heavy Ball method, can be viewed as a dynamical…

Using the concept of dynamical mappings, two symmetry conserving nonperturbative approaches are presented. The first is based on the 1/N-expansion and sorted out using Holstein-Primakoff mapping. The second consists of dynamically mapping…