The present paper deals with the geometry of the tangent bundle over a differentiable (Cr)
manifold, and with the so-called inverse problem of Lagrangian dynamics. There are various …

The study of (nonlinear) dift" erential equations was S. Lie's motivation when he created
what is now known as Lie groups and Lie algebras; nevertheless, although Lie group and …

We consider a dynamical system moving in a Riemannian space and prove two theorems
which relate the Lie point symmetries and Noether symmetries of the equation of motion …

A theorem is proved that determines the first integrals of the form I= K ab (t, q) q ̇ aq ̇ b+ K
a (t, q) q ̇ a+ K (t, q) of autonomous holonomic systems using only the collineations of the …

A detailed symmetry analysis is performed for a microscopic model used to describe traffic
flow in two-lane motorways. The traffic flow theory employed in this model is a two …

We study the generalized symmetries of the Lorenz model to find the parameter values at
which one or more time-dependent integrals of motion exist. In these cases the integrals are …

We consider the generic quadratic first integral (QFI) of the form I= K ab (t, q) q˙ aq˙ b+ K a (t,
q) q˙ a+ K (t, q) and require the condition d I/dt= 0. The latter results in a system of partial …

The complete symmetry group classification of the fourth-order Euler–Bernoulli ordinary
differential equation, where the elastic modulus and the area moment of inertia are …

We discuss the relation between Noether (point) symmetries and discrete symmetries for a
class of minisuperspace cosmological models. We show that when a Noether symmetry …

We determine the autonomous three-dimensional Newtonian systems which admit Lie point
symmetries and the three-dimensional autonomous Newtonian Hamiltonian systems which …