Invariants for certain discrete dynamical systems given by rational mappings

  1. Ignacio Bajo 1
  1. 1 Universidade de Vigo
    info

    Universidade de Vigo

    Vigo, España

    ROR https://ror.org/05rdf8595

Zeitschrift:
Qualitative theory of dynamical systems

ISSN: 1575-5460

Datum der Publikation: 2017

Ausgabe: 16

Nummer: 3

Seiten: 467-490

Art: Artikel

Andere Publikationen in: Qualitative theory of dynamical systems

Zusammenfassung

We study the existence of invariants for the family of systems in an open domain D of Rn or Cn whose components are linear fractionals sharing denominator. Such systems can be written with the aid of homogeneous coordinates as the composition of a linear map in Kn+1 with a certain projection and their behaviour is strongly determined by the spectral properties of the corresponding linear map.The paper is committed to prove that if n ≥ 2 then every system of this kind admits an invariant, both in the real and in the complex case. In fact, for a sufficiently large n several functionally independent invariants can be obtained and, in many cases, the invariant can be chosen as the quotient of two quadratic polynomials.

Informationen zur Finanzierung

This research has been supported by the Spanish Government and FEDER, grant

Geldgeber