Related papers: Dynamical Similarity in Higher-Order Classical Sym…
A natural and very important development of constrained system theory is a detail study of the relation between the constraint structure in the Hamiltonian formulation with specific features of the theory in the Lagrangian formulation,…
Dynamical similarities are non-standard symmetries found in a wide range of physical systems that identify solutions related by a change of scale. In this paper we will show through a series of examples how this symmetry extends to the…
We examine "dynamical similarities" in the Lagrangian framework. These are symmetries of an intrinsically determined physical system under which observables remain unaffected, but the extraneous information is changed. We establish three…
We study a long-recognised but under-appreciated symmetry called "dynamical similarity" and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a…
Simple examples are used to introduce and examine symmetries of open quantum dynamics that can be described by unitary operators. For the Hamiltonian dynamics of an entire closed system, the symmetry takes the expected form which, when the…
Contact reduction is very closely related to symplectic reduction, but it allows symmetries that are not manifest in Hamiltonian mechanics and moreover, solution of the reduced problems yields solution of the original problem without…
This paper explores the relationship between Cartan symmetries, dynamical similarities, and dynamical symmetries in contact Hamiltonian mechanics. By introducing an alternative decomposition of vector fields, we characterize these…
The strict connection between Lie point-symmetries of a dynamical system and its constants of motion is discussed and emphasized, through old and new results. It is shown in particular how the knowledge of a symmetry of a dynamical system…
In contact Hamiltonian systems, the so-called dissipated quantities are akin to conserved quantities in classical Hamiltonian systems. In this paper, we prove a Noether's theorem for non-autonomous contact Hamiltonian systems,…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
A complete geometric classification of symmetries of autonomous Hamiltonian mechanical systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results…
The symmetry reduction of dynamical systems that are invariant under changes of global scale is well-understood for classical theories of particles, and fields. The excision of the superfluous degree of freedom generating such rescalings…
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 investigate various types of symmetries and their mutual relationships in Hamiltonian systems defined on manifolds with different geometric structures: symplectic, cosymplectic, contact and cocontact. In each case we pay special…
It is shown that all spherical symmetric potentials are capable of producing dynamical symmetries in classical one-body motions, thanks to the inevitable existence of symmetry axes associated with turning points for corresponding…
Symmetry under a particular class of non-strictly canonical transformation may be used to identify, and subsequently excise degrees of freedom which do not contribute to the closure of the algebra of dynamical observables. Such redundant…
Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…
This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description…
One of the foremost goals of research in physics is to find the most basic and universal theories that describe our universe. Many theories assume the presence of an absolute space and time in which the physical objects are located and…
Several interesting physical systems, such as the Lovelock extension of General Relativity in higher dimensions, classical time crystals, k-essence fields, Horndeski theories, compressible fluids, and nonlinear electrodynamics, have…