TY - JOUR
T1 - Periodic points of a Landen transformation
AU - Gasull, Armengol
AU - Llorens, Mireia
AU - Mañosa, Víctor
PY - 2018/11/1
Y1 - 2018/11/1
N2 - © 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.
AB - © 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.
KW - Landen transformation
KW - Periodic points
KW - Poincaré–Miranda theorem
UR - https://ddd.uab.cat/record/199367
U2 - https://doi.org/10.1016/j.cnsns.2018.04.020
DO - https://doi.org/10.1016/j.cnsns.2018.04.020
M3 - Article
VL - 64
SP - 232
EP - 245
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
SN - 1007-5704
ER -