© 2018 Elsevier B.V. We prove the existence of 3-periodic orbits in a dynamical system associated to a Landen transformation previously studied by Boros, Chamberland and Moll, disproving a conjecture on the dynamics of this planar map introduced by the latter author. To this end we present a systematic methodology to determine and locate analytically isolated periodic points of algebraic maps. This approach can be useful to study other discrete dynamical systems with algebraic nature. Complementary results on the dynamics of the map associated with the Landen transformation are also presented.
|Journal||Communications in Nonlinear Science and Numerical Simulation|
|Publication status||Published - 1 Nov 2018|
- Landen transformation
- Periodic points
- Poincaré–Miranda theorem