Periodic points of a Landen transformation
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 de...
| Authors: | , , |
|---|---|
| Format: | article |
| Publication Date: | 2018 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/117414 |
| Online Access: | https://hdl.handle.net/2117/117414 https://dx.doi.org/10.1016/j.cnsns.2018.04.020 |
| Access Level: | Open access |
| Keyword: | Differentiable dynamical systems Periodic points Landen transformations Poincaré-Miranda theorem Sistemes dinàmics diferenciables Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory Classificació AMS::33 Special functions::33E Other special functions Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics |
| Summary: | 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. |
|---|