About the Algebraic Yuzvinski Formula

• Autorzy: Anna Giordano Bruno , Simone Virili
• Języki publikacji: EN

Abstrakty

EN

The Algebraic Yuzvinski Formula expresses the algebraic entropy of an endomorphism of a finitedimensional rational vector space as the Mahler measure of its characteristic polynomial. In a recent paper, we have proved this formula, independently fromits counterpart – the Yuzvinski Formula – for the topological entropy proved by Yuzvinski in 1968. In this paper we first compare the proof of the Algebraic Yuzvinski Formula with a proof of the Yuzvinski Formula given by Lind and Ward in 1988, underlying the common ideas and the differences in the main steps. Then we describe several known applications of the Algebraic Yuzvinski Formula, and some related open problems are discussed. Finally,we give a new and purely algebraic proof of the Algebraic Yuzvinski Formula for the intrinsic algebraic entropy.

Słowa kluczowe

EN

algebraic entropy; topological entropy; endomorphism; Yuzvinski Formula; intrinsic entropy

• Wydawca: De Gruyter Open
• Czasopismo: Topological Algebra and its Applications
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-07-11

zaakceptowano

2015-08-30

online

2015-11-26

Twórcy

autor

Anna Giordano Bruno

• Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, 33100 Udine,
  Italia

autor

Simone Virili

• Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Trieste 63,
  35121 Padova, Italia

Bibliografia

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Identyfikatory

DOI

10.1515/taa-2015-0008