TY - JOUR
T1 - Dynamics of a Lotka-Volterra map
AU - Balibrea, Francisco
AU - Guirao, Juan Luis García
AU - Lampart, Marek
AU - Llibre, Jaume
PY - 2006/11/13
Y1 - 2006/11/13
N2 - Given the plane triangle with vertices (0, 0), (0, 4) and (4, 0) and the transformation F : (x, y) → (x(4 - x - y), xy) introduced by A. N. Sharkovskiǐ, we prove the existence of the following objects: a unique invariant curve of spiral type, a periodic trajectory of period 4 (given explicitly) and a periodic trajectory of period 5 (described approximately). Also, we give a decomposition of the triangle which helps to understand the global dynamics of this discrete system which is linked with the behavior of the Schrödinger equation.
AB - Given the plane triangle with vertices (0, 0), (0, 4) and (4, 0) and the transformation F : (x, y) → (x(4 - x - y), xy) introduced by A. N. Sharkovskiǐ, we prove the existence of the following objects: a unique invariant curve of spiral type, a periodic trajectory of period 4 (given explicitly) and a periodic trajectory of period 5 (described approximately). Also, we give a decomposition of the triangle which helps to understand the global dynamics of this discrete system which is linked with the behavior of the Schrödinger equation.
KW - Periodic trajectory
KW - Resultant
KW - Spiral type curve
U2 - https://doi.org/10.4064/fm191-3-5
DO - https://doi.org/10.4064/fm191-3-5
M3 - Article
VL - 191
SP - 265
EP - 279
JO - Fundamenta Mathematicae
JF - Fundamenta Mathematicae
SN - 0016-2736
ER -