Dynamics of a Lotka-Volterra map

Francisco Balibrea, et al. "Dynamics of a Lotka-Volterra map." Fundamenta Mathematicae 191.3 (2006): 265-279. <http://eudml.org/doc/282668>.

@article{FranciscoBalibrea2006,
abstract = {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. Sharkovskiĭ, 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.},
author = {Francisco Balibrea, Juan Luis García Guirao, Marek Lampart, Jaume Llibre},
journal = {Fundamenta Mathematicae},
keywords = {spiral type curve; periodic trajectory; resultant; invariant set},
language = {eng},
number = {3},
pages = {265-279},
title = {Dynamics of a Lotka-Volterra map},
url = {http://eudml.org/doc/282668},
volume = {191},
year = {2006},
}

TY - JOUR
AU - Francisco Balibrea
AU - Juan Luis García Guirao
AU - Marek Lampart
AU - Jaume Llibre
TI - Dynamics of a Lotka-Volterra map
JO - Fundamenta Mathematicae
PY - 2006
VL - 191
IS - 3
SP - 265
EP - 279
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. Sharkovskiĭ, 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.
LA - eng
KW - spiral type curve; periodic trajectory; resultant; invariant set
UR - http://eudml.org/doc/282668
ER -