Abelian groups of zero adjoint entropy

L. Salce¹ ; P. Zanardo¹

¹ Dipartimento di Matematica Pura e Applicata Università di Padova Via Trieste 63 35121 Padova, Italy

Colloquium Mathematicum, Tome 121 (2010) no. 1, pp. 45-62

Résumé

The notion of adjoint entropy for endomorphisms of an Abelian group is somehow dual to that of algebraic entropy. The Abelian groups of zero adjoint entropy, i.e. ones whose endomorphisms all have zero adjoint entropy, are investigated. Torsion groups and cotorsion groups satisfying this condition are characterized. It is shown that many classes of torsionfree groups contain groups of either zero or infinite adjoint entropy. In particular, no characterization of torsionfree groups of zero adjoint entropy is possible. It is also proved that the mixed groups of a wide class all have infinite adjoint entropy.

Détail

DOI : 10.4064/cm121-1-5

Keywords: notion adjoint entropy endomorphisms abelian group somehow dual algebraic entropy abelian groups zero adjoint entropy whose endomorphisms have zero adjoint entropy investigated torsion groups cotorsion groups satisfying condition characterized shown many classes torsionfree groups contain groups either zero infinite adjoint entropy particular characterization torsionfree groups zero adjoint entropy possible proved mixed groups wide class have infinite adjoint entropy autors autor aaa aaa adr dipartimento matematica pura applicata universit padova via trieste padova italy adr eml salce math unipd eml lne *salce lne autor autor aaa aaa adr dipartimento matematica pura applicata universit padova via trieste padova italy adr eml pzanardo math unipd eml lne *zanardo lne autor autors abelian groups zero adjoint entropy entry * entry chainable continuum homeomorphisms rightarrow constructed following properties circ circ have simple dynamics circ positively continuum wise fully expansive homeomorphism has positive entropy chaotic sense devaney sense yorke