Related papers: Symmetries of dynamical systems and convergent nor…
We outline a new, systematic way of constructing and analysing field theories, where all possible continuous symmetries of a given model are derived using the method of Lie point symmetries. If the model has free parameters, and…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
The existence of point symmetries in the cosmological field equations of generalized vacuum scalar--tensor theories is considered within the context of the spatially homogeneous cosmologies. It is found that such symmetries only occur in…
In this paper a symplectic realization for the Maxwell-Bloch equations with the rotating wave approximation is given, which also leads to a Lagrangian formulation. We show how Lie point symmetries generate a third constant of motion for the…
A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and on the lattice. They take solutions into solutions and can be…
We consider free and proper cotangent-lifted symmetries of Hamiltonian systems. For the special case of G = SO(3), we construct symplectic slice coordinates around an arbitrary point. We thus obtain a parametrisation of the phase space…
We consider a system of partial differential equations, of interest to plasma physics, and provide all its Lie point symmetries, with their respective invariant solutions. We also discuss some of its conditional and partial symmetries. We…
We study continuous groups of generalized Kerr-Schild transformations and the vector fields that generate them in any n-dimensional manifold with a Lorentzian metric. We prove that all these vector fields can be intrinsically characterized…
Noether's theorem provides a powerful link between continuous symmetries and conserved quantities for systems governed by some variational principle. Perhaps unfortunately, most dynamical systems of interest in neuroscience and artificial…
Many features of physical systems, both qualitative and quantitative, become sharply defined or tractable only in some limiting situation. Examples are phase transitions in the thermodynamic limit, the emergence of classical mechanics from…
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…
We establish Ecalle's mould calculus in an abstract Lie-theoretic setting and use it to solve a normalization problem, which covers several formal normal form problems in the theory of dynamical systems. The mould formalism allows us to…
In this paper, we study infinite dimensional holomorphic vector fields on sequence spaces, having a fixed point at $0$. Under suitable hypotheses we prove the existence of analytic invariant submanifolds passing through the fixed point. The…
In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…
The suggested approach makes it possible to produce a consistent description of motions of a physical system. It is shown that the concept of force fields defining the systems dynamics is equivalent to the choice of the corresponding metric…
Different symmetry formalisms for difference equations on lattices are reviewed and applied to perform symmetry reduction for both linear and nonlinear partial difference equations. Both Lie point symmetries and generalized symmetries are…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
If two control systems on manifolds of the same dimension are dynamic equivalent, we prove that either they are static equivalent --i.e. equivalent via a classical diffeomorphism-- or they are both ruled; for systems of different…
In this paper we present the theorem on Lie integrability by quadratures for time-independent Hamiltonian systems on symplectic and contact manifolds, and for time-dependent Hamiltonian systems on cosymplectic and cocontact manifolds. We…
We briefly review the various contexts within which one might address the issue of ``why'' the dimensionless constants of Nature have the particular values that they are observed to have. Both the general historical trend, in physics, of…