Related papers: Infinitesimal symmetries in Contact Hamiltonian sy…
We discuss the Hamiltonian dynamics for cosmologies coming from Extended Theories of Gravity. In particular, minisuperspace models are taken into account searching for Noether symmetries. The existence of conserved quantities gives…
The Noether symmetry issue for Horndeski Lagrangian has been studied. We have been proven a series of theorems about the form of Noether conserved charge (current) for irregular (not quadratic) dynamical systems. Special attentions have…
Following the analysis we have presented in a previous paper (that we refer to as [I]), we describe a Noether theorem related to symmetries, with the associated reduction procedures, for classical dynamics within the Lagrangian and the…
We present new relations derived from Noether's identity that reveal the compatibility between the components of the Hessian matrix of the Lagrangian, the infinitesimal symmetry transformation of the configuration variables and time, and a…
For difference variational problems on lattice, this paper presents a relation between divergence variational symmetries and conservation laws for the associated Euler-Lagrange system provided by Noether's theorem. This hence inspires us to…
For k-symplectic Hamiltonian field theories, we study infinitesimal transformations generated by certain kinds of vector fields which are not Noether symmetries, but which allow us to obtain conservation laws by means of a suitable…
Starting from the geometric description of quantum systems, we propose a novel approach to time-independet dissipative quantum processes according to which the energy is dissipated but the coherence of the states is preserved. Our proposal…
The phase space of relativistic particle mechanics is defined as the 1st jet space of motions regarded as timelike 1-dimensional submanifolds of spacetime. A Lorentzian metric and an electromagnetic 2-form define naturally on the…
In this paper we address the problem of identifying contracting systems among dynamical systems appearing in mechanics. First, we introduce a sufficient condition to identify contracting systems in a general Riemannian manifold. Then, we…
We analyze all possible symmetry reductions of Lagrangians that yield fully equivalent field equations for any 4-dimensional metric theory of gravity. Specifically, we present a complete list of infinitesimal group actions obeying the…
Noether's theorem, which connects continuous symmetries to exact conservation laws, remains one of the most fundamental principles in physics and dynamical systems. In this work, we draw a conceptual parallel between two paradigms: the…
We extend Noether's theorem to the setting of multisymplectic geometry by exhibiting a correspondence between conserved quantities and continuous symmetries on a multi-Hamiltonian system. We show that a homotopy co-momentum map interacts…
We introduce an generalized action functional describing the equations of motion and the variational equations for any Lagrangian system. Using this novel scheme we are able to generalize Noether's theorem in such a way that to any…
The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is…
Infinitesimal symmetries of a partial differential equation (PDE) can be defined algebraically as the solutions of the linearization (Frechet derivative) equation holding on the space of solutions to the PDE, and they are well-known to…
In this paper we show how the well-know local symmetries of Lagrangeans systems, and in particular the diffeomorphism invariance, emerge in the Hamiltonian formulation. We show that only the constraints which are linear in the momenta…
This paper expounds the modern theory of symplectic reduction in finite-dimensional Hamiltonian mechanics. This theory generalizes the well-known connection between continuous symmetries and conserved quantities, i.e. Noether's theorem. It…
We formulate and study a generalized virial theorem for contact Hamiltonian systems. Such systems describe mechanical systems in the presence of simple dissipative forces such as Rayleigh friction, or the vertical motion of a particle…
The aim of this note is to discuss the relation between one-parameter continuous symmetries of the dynamics, defined on physical grounds, and conservation laws. In the Hamiltonian formulation, such symmetries of the dynamics in general…
A generalization of the KP equation involving higher-order dispersion is studied. This equation appears in several physical applications. As new results, the Lie point symmetries are obtained and used to derive conservation laws via…