Existence theorem for weak quasiperiodic solutions of Lagrangian systems on Riemannian manifolds

TL;DR

This paper proves new conditions under which weak quasiperiodic solutions exist for Lagrangian systems on Riemannian manifolds with quasiperiodic forcing, expanding understanding of such dynamical systems.

Contribution

It introduces novel sufficient conditions for the existence of weak quasiperiodic solutions in Lagrangian systems on Riemannian manifolds.

Findings

Established existence of weak Besicovitch quasiperiodic solutions

Derived new sufficient conditions for solutions' existence

Extended results to systems with time-quasiperiodic forces

Abstract

We establish new sufficient conditions for the existence of weak Besicovitch quasiperiodic solutions for natural Lagrangian system on Riemannian manifold with time-quasiperiodic force function