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arXiv · 1801.04195

Periodic points of a Landen transformation

Armengol Gasull·Mireia Llorens·Víctor Mañosa
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Abstract

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.

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Armengol Gasull, Mireia Llorens, Víctor Mañosa. 2018-01-12. Periodic points of a Landen transformation. https://doi.org/10.1016/j.cnsns.2018.04.020

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