相关论文: Singular reduction of implicit Hamiltonian systems

The aim of this paper is to develop a constraint algorithm for singular classical field theories in the framework of $k$-cosymplectic geometry. Since these field theories are singular, we need to introduce the notion of $k$-precosymplectic…

We review the concept of the (anomalous) Poisson-Lie symmetry in a way that emphasises the notion of Poisson-Lie Hamiltonian. The language that we develop turns out to be very useful for several applications: we prove that the left and the…

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…

We develop a theory of "quasi"-Hamiltonian G-spaces for which the moment map takes values in the group G itself rather than in the dual of the Lie algebra. The theory includes counterparts of Hamiltonian reductions, the Guillemin-Sternberg…

The singularity structure of solutions of a class of Hamiltonian systems of ordinary differential equations in two dependent variables is studied. It is shown that for any solution, all movable singularities, obtained by analytic…

We consider solutions of the $2\times 2$ matrix Hamiltonian of physical systems within the context of the asymptotic iteration method. Our technique is based on transformation of the associated Hamiltonian in the form of the first order…

This paper explains the recent developments on the symplectic theory of Hamiltonian completely integrable systems on symplectic 4-manifolds, compact or not. One fundamental ingredient of these developments has been the understanding of…

The main goal of these lectures is to introduce and review the Hamiltonian formalism for classical constrained systems and in particular gauge theories. Emphasis is put on the relation between local symmetries and constraints and on the…

The aim of this paper is to present an explicit reduction algorithm for Hilbert modular groups over arbitrary totally real number fields. An implementation of the algorithm is available to download from [19]. The exposition is…

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…

Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…

In this paper, for a variety of nonholonomic (reducible) Hamiltonian systems, we first give to various distributional Hamiltonian systems, by analyzing carefully the dynamics and structures of the nonholonomic Hamiltonian systems. Secondly,…

In this paper, we present a generalization of a Hamilton--Jacobi theory to higher order implicit differential equations. We propose two different backgrounds to deal with higher order implicit Lagrangian theories: the Ostrogradsky approach…

In this paper, we introduce the notion of a multiplicative unimodularity for a coisotropic Poisson homogeneous space. Then, we discuss the unimodularity and the multiplicative unimodularity for these spaces and the existence of an invariant…

We consider symplectic singularities in the sense of A. Beauville as examples of Poisson schemes. Using Poisson methods, we prove that a symplectic singularity admits a finite stratification with smooth symplectic strata. We also prove that…

Hamilton's equations with noise and friction possess a hidden supersymmetry, valid for time-independent as well as periodically time-dependent systems. It is used to derive topological properties of critical points and periodic trajectories…

By the method of discrete transformation equations of 3-th wave hierarchy are constructed. We present in explicit form two Poisson structures, which allow to construct Hamiltonian operator consequent application of which leads to all…

This work presents the basic elements of the formalism involved in the treatment of Hamiltonian dynamical systems with symmetry and the geometrical description of collective motion.

We first exhibit two compatible Poisson structures on the cotangent bundle of the unitary group $\mathrm{U}(n)$ in such a way that the invariant functions of the $\mathfrak{u}(n)^*$-valued momenta generate a bi-Hamiltonian hierarchy. One of…

We study in this work the important class of nonlocal Poisson Brackets (PB) which we call weakly nonlocal. They appeared recently in some investigations in the Soliton Theory. However there was no theory of such brackets except very special…