The algebraic entropy h defined for endomorphisms f of abelian groups G measures the growth of the trajectories of non-empty finite subsets F of G with respect to f. We show that this growth can be either polynomial or exponential. The greatest f-invariant subgroup of G where this growth is polynomial coincides with the greatest f-invariant subgroup P(G,f) of G (named Pinsker subgroup of f) such that h(f|_P(G,f))=0. We obtain also an alternative characterization of P(G,f) from the point of view of the quasi-periodic points of f.

The Pinsker subgroup of an algebraic flow

DIKRANJAN, Dikran;GIORDANO BRUNO, Anna
2012-01-01

Abstract

The algebraic entropy h defined for endomorphisms f of abelian groups G measures the growth of the trajectories of non-empty finite subsets F of G with respect to f. We show that this growth can be either polynomial or exponential. The greatest f-invariant subgroup of G where this growth is polynomial coincides with the greatest f-invariant subgroup P(G,f) of G (named Pinsker subgroup of f) such that h(f|_P(G,f))=0. We obtain also an alternative characterization of P(G,f) from the point of view of the quasi-periodic points of f.
File in questo prodotto:
File Dimensione Formato  
IRIS-pinsker.pdf

Open Access dal 02/03/2016

Descrizione: Articolo principale
Tipologia: Documento in Post-print
Licenza: Creative commons
Dimensione 383.86 kB
Formato Adobe PDF
383.86 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/881020
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 22
  • ???jsp.display-item.citation.isi??? 19
social impact