Invariants for certain discrete dynamical systems given by rational mappings
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Universidade de Vigo
info
ISSN: 1575-5460
Année de publication: 2017
Volumen: 16
Número: 3
Pages: 467-490
Type: Article
D'autres publications dans: Qualitative theory of dynamical systems
Résumé
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.
Information sur le financement
This research has been supported by the Spanish Government and FEDER, grantFinanceurs
- European Regional Development Fund European Union