A+ CATEGORY SCIENTIFIC UNIT

Dynamics of a Lotka–Volterra map

Volume 191 / 2006

Francisco Balibrea, Juan Luis García Guirao, Marek Lampart, Jaume Llibre Fundamenta Mathematicae 191 (2006), 265-279 MSC: Primary 58F13. DOI: 10.4064/fm191-3-5

Abstract

Given the plane triangle with vertices $(0,0)$, $(0,4)$ and $(4,0)$ and the transformation $F:(x,y) \mapsto (x(4-x-y),xy)$ introduced by A. N. Sharkovski\uı, 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.

Authors

  • Francisco BalibreaDepartamento de Matemáticas
    Universidad de Murcia
    30100 Murcia (Región de Murcia), Spain
    e-mail
  • Juan Luis García GuiraoDepartamento de Matemática
    Aplicada y Estadística
    Universidad Politécnica de Cartagena
    C/ Paseo Alfonso XIII
    30203 Cartagena (Región de Murcia), Spain
    e-mail
  • Marek LampartMathematical Institute at Opava
    Silesian University at Opava
    Na Rybníčku 1 1
    746 01 Opava, Czech Republic
    e-mail
  • Jaume LlibreDepartament de Matemátiques
    Universitat Autónoma de Barcelona
    Bellaterra, 08193 Barcelona (Catalunya), Spain
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image