On the global dynamics of periodic triangular maps

TL;DR

This paper extends the understanding of global dynamics from autonomous to periodic non-autonomous triangular maps, establishing conditions for convergence to fixed points or periodic orbits based on the absence of certain prime period orbits.

Contribution

It generalizes previous results on autonomous maps to periodic non-autonomous maps, providing criteria for convergence to fixed points or periodic orbits.

Findings

Orbit convergence depends on absence of prime period orbits

Conditions for convergence to fixed points or periodic orbits

Extension of autonomous map results to periodic non-autonomous maps

Abstract

This paper is an extension of an earlier paper that dealt with global dynamics in autonomous triangular maps. In the current paper, we extend the results on global dynamics of autonomous triangular maps to periodic non-autonomous triangular maps. We show that, under certain conditions, the orbit of every point in a periodic non-autonomous triangular map converges to a fixed point (respectively, periodic orbit of period $p$) if and only if there is no periodic orbit of prime period two (respectively, periodic orbits of prime period greater than $p$).