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

Aldizkaria:
Qualitative theory of dynamical systems

ISSN: 1575-5460

Argitalpen urtea: 2017

Alea: 16

Zenbakia: 3

Orrialdeak: 467-490

Mota: Artikulua

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Beste argitalpen batzuk: Qualitative theory of dynamical systems

Laburpena

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.

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

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