Exactness of Lepage 2-forms and globally variational differential equations

The exactness equation for Lepage [Formula: see text]-forms, associated with variational systems of ordinary differential equations on smooth manifolds, is analyzed with the aim to construct a concrete global variational principle. It is shown that locally variational systems defined by homogeneous functions of degree [Formula: see text] are automatically globally variational. A new constructive method of finding a global Lagrangian is described for these systems, which include for instance the geodesic equations in Riemann and Finsler geometry.

Splitting with Different Growth Rates for Linear Discrete-time Skew-evolution Semiflows in Banach Spaces

In this paper we intend to study three concepts of (h, k)-splitting for skew-evolution semiflows, which model discrete-time variational systems in Banach spaces. We also aim to give connections between them, emphasized by counterexamples and we propose an open problem.