We review the general theory of the Jacobi last multipliers in geometric terms and then apply
the theory to different problems in integrability and the inverse problem for one-dimensional …

Lie systems form a class of systems of first-order ordinary differential equations whose
general solutions can be described in terms of certain finite families of particular solutions …

The two-dimensional inverse problem for first-order systems is analysed and a method to
construct an affine Lagrangian for such systems is developed. The determination of such …

This work concerns the definition and analysis of a new class of Lie systems on Poisson
manifolds enjoying rich geometric features: the Lie–Hamilton systems. We devise methods …

A Lie system is a system of first-order ordinary differential equations describing the integral
curves of a t-dependent vector field taking values in a finite-dimensional real Lie algebra of …

Time and again, non-conventional forms of Lagrangians with non-quadratic velocity
dependence have received attention in the literature. For one thing, such Lagrangians have …

Constants of motion, Lagrangians, and Hamiltonians admitted by a family of relevant
nonlinear oscillators are derived using a geometric formalism. The theory of the Jacobi last …

Lie symmetry analysis is one of the powerful tools to analyse nonlinear ordinary differential
equations. We review the effectiveness of this method in terms of various symmetries. We …

In this work we establish the relation between the Jacobi last multiplier, which is a
geometrical tool in the solution of problems in mechanics and that provides Lagrangian …

A superposition rule is a particular type of map that enables one to express the general
solution of certain systems of first-order ordinary differential equations, the so-called Lie …