On the affine-periodic solutions of discrete dynamical systems

Random Periodic Solutions of Random Dynamical Systems

Similar to the deterministic dynamical systems, in stochastic dynamical systems, the problem of the long time or infinite horizon behaviour is a fundamental problem occupying a central place of research. Studies of dynamic properties of such systems, both deterministic and stochastic, usually involve an appropriate definition of a steady state (viewed as a dynamic equilibrium) and conditions th...

On the periodic solutions of discrete Hamiltonian systems

Almost all numerical methods for solving conservative problems cannot avoid a more or less perceptible drift phenomenon. Considering that the drift would be absent on a periodic or quasi-periodic solution, one way to eliminate such unpleasant phenomenon is to look for discrete periodic or quasi-periodic solutions. It is quite easy to show that only symmetric methods are able to provide solution...

Periodic Solutions of Second-order Nonautonomous Dynamical Systems

Periodic solutions of second order non-autonomous singular dynamical systems

In this paper, we establish two different existence results of positive periodic solutions for second order non-autonomous singular dynamical systems. The first one is based on a nonlinear alternative principle of Leray–Schauder and the result is applicable to the case of a strong singularity as well as the case of a weak singularity. The second one is based on Schauder’s fixed point theorem an...

Convergence Time towards Periodic Orbits in Discrete Dynamical Systems

We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we use linearized equations to examine the evolution near that neighborhood. The underlying idea is that points of stable periodic orbit are associated with in...