Systems of second-order ordinary differential equations admitting a Lagrangian formulation are deformed requiring that the extended Lagrangian preserves a fixed subalgebra of Noether symmetries of the original system. For the case of the simple Lie algebra sl(2,R), this provides non-linear systems with two independent constants of the motion quadratic in the velocities. In the case of scalar di...

We study a generalized non-local theory of gravity which, in specific limits, can become either the curvature non-local or teleparallel non-local theory. Using the Noether symmetry approach, we find that the coupling functions coming from the non-local terms are constrained to be either exponential or linear in form. It is well known that in some non-local theories, a certain kind of exponentia...

The generalized Killing equations and the symmetries of Taub-NUT spinning space are investigated. For spinless particles the Runge-Lenz vector defines a constant of motion directly, whereas for spinning particles it now requires a non-trivial contribution from spin. The generalized Runge-Lenz vector for spinning Taub-NUT space is completely evaluated. PACS. 04.20.Me Conservation laws and equati...

It is shown that the compactification á la Randall-Sundrum of so-called, five-dimensional Einstein-Chern-Simons action gravity leads to an for a four-dimensional scalar-tensor includes Gauss-Bonnet term, which belongs particular case Horndeski theory. The new gravitational degrees freedom were introduced requiring be invariant under symmetries greater than usual Poincaré or (A)dS symmetries, na...

In this work, a complete classification of the Lie group symmetries for generalization Chazy equation was carried out and equivalence generalized is calculated used to present principal algebra equation.

We compute the extension of the Lagrangian of N = 1 supersymmetric theories to the case in which some axion symmetries are gauged. It turns out that generalized Chern–Simons terms appear that were not considered in previous superspace formulations of general N = 1 theories. Such gaugings appear in supergravities arising from flux compactifications of superstrings, as well as from Scherk–Schwarz...

We consider generalized (possibly depending on fields as well as on space-time variables) gauge transformations and gauge symmetries in the context of general – that is, possibly non variational nor covariant – differential equations. In this case the relevant principal bundle admits the first jet bundle (of the phase manifold) as an associated bundle, at difference with standard Yang-Mills the...

Reduced Ermakov systems are defined as Ermakov systems restricted to the level surfaces of the Ermakov invariant. The condition for Lie point symmetries for reduced Ermakov systems is solved yielding four infinite families of systems. It is shown that SL(2, R) always is a group of point symmetries for the reduced Ermakov systems. The theory is applied to a model example and to the equations of ...