Linear instability for periodic orbits of non-autonomous Lagrangian systems

Relative Periodic Orbits of Symmetric Lagrangian Systems

MULTIPLE PERIODIC SOLUTIONS FOR A CLASS OF NON-AUTONOMOUS AND CONVEX HAMILTONIAN SYSTEMS

In this paper we study Multiple periodic solutions for a class of non-autonomous and convex Hamiltonian systems and we investigate use some properties of Ekeland index.  

Existence of Periodic Orbits for High-dimensional Autonomous Systems

We give a result on existence of periodic orbits for autonomous differential systems with arbitrary finite dimension. It is based on a Poincaré-Bendixson property enjoyed by a new class of monotone systems introduced in L. A. Sanchez, Cones of rank 2 and the PoincaréBendixson property for a new class of monotone systems, Journal of Differential Equations 216 (2009), 1170-1190. A concrete applic...

Non-linear Instability of Periodic Orbits of Suspensions of Thin Fibers in Fluids

It is known that Jeffery’s equation predicts that fibers with Jeffery’s parameter less than one will exhibit periodic behavior when subjected to shear flows. Yet this behavior is not seen in suspensions containing many fibers. This paper explores the extent to which coupling Jeffery’s equation with the viscosity of the suspension causes instability that breaks up this periodic behavior. A simpl...

Existence of Periodic Orbits in Completed Lagrangian Hybrid Systems with Non-Plastic Collisions

In this paper, we consider hybrid models of mechanical systems undergoing impacts, i.e., Lagrangian hybrid systems, and study their periodic orbits in the presence of Zeno behavior. The main result of this paper is explicit conditions under which the existence of stable periodic orbits for a Lagrangian hybrid system with plastic impacts implies the existence of periodic orbits in the same Lagra...