Orbitas frenadas en sistemas mecánicos finslerianos

Abstract

Given a mechanical system (M,K,U) where M is a n-dimensional variety and the kinetic and potential energy K and U are three times differentiable, let E0 be a potential energy value such that {X ϵ M|U(x) ≤ E0} is homeomorphic to the n-dimensional disk, and its border B is the E0-equipotential surface. If (M,K,U) is a Finsler mechanical system, then any point of potential energy less than E0 can be joined to B by an orbit of total energy E0 which approaches a fixed point of B. If (M,K,U) is a Riemann mechanical system, the orbit can be made to turn back on itself after reaching B.