Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/de-gruyter/about-the-algebraic-yuzvinski-formula-DUgme00M62
References (41)
-
D. Toller, Simone Virili (2019)
ERRATA CORRIGE: Intrinsic algebraic entropyarXiv: Group Theory
-
D. Dikranjan, M. Sanchis, Simone Virili (2012)
New and old facts about entropy in uniform spaces and topological groupsTopology and its Applications, 159
-
D. Lehmer (1933)
Factorization of Certain Cyclotomic FunctionsAnnals of Mathematics, 34
-
P. Walters (1977)
Introduction to Ergodic Theory -
R. Bowen (1971)
Entropy for group endomorphisms and homogeneous spacesTransactions of the American Mathematical Society, 153
-
A. Bruno, Simone Virili (2011)
Algebraic Yuzvinski FormulaarXiv: Group Theory
-
C. Smyth (2007)
Number Theory and Polynomials: The Mahler measure of algebraic numbers: a surveyarXiv: Number Theory
-
D. Dikranjan, A. Bruno (2013)
The Bridge Theorem for totally disconnected LCA groupsarXiv: General Topology
-
D. Dikranjan, A. Bruno (2013)
Topological Entropy and Algebraic Entropy for group endomorphismsarXiv: General Topology
-
K. Mahler (1962)
On Some Inequalities for Polynomials in Several VariablesJournal of The London Mathematical Society-second Series
-
Yuzvinski (1965)
Metric properties of endomorphisms of compact groups Mat in TranslationAcad English Amer Math Soc Transl, 29
-
D. Dikranjan, A. Bruno (2010)
The Pinsker subgroup of an algebraic flowarXiv: Group Theory
-
Yuzvinski (1967)
Computing the entropy of a group endomorphism Sibirsk Mat in TranslationEnglish Siberian Math J, 8
-
Dikranjan (2015)
Intrinsic algebraic entropyPure Appl Algebra
-
Simone Virili (2012)
Entropy for endomorphisms of LCA groupsTopology and its Applications, 159
-
Dikranjan (2012)
Limit free computation of entropy RendIstit Mat Univ Trieste
-
J. Peters (1981)
ENTROPY OF AUTOMORPHISMS ON L.C.A. GROUPSPacific Journal of Mathematics, 96
-
Michael Weiss (1974)
Algebraic and other entropies of group endomorphismsMathematical systems theory, 8
-
M. Einsiedler, T. Ward (2010)
Ergodic Theory: with a view towards Number Theory -
A. Weil (1967)
Basic number theory -
L. Kronecker
Zwei Sätze über Gleichungen mit ganzzahligen Coefficienten.Journal für die reine und angewandte Mathematik (Crelles Journal), 1857
-
Peters (1981)
Entropy of automorphisms on groups Pacific noMath
-
D. Dikranjan, A. Bruno (2012)
The connection between topological and algebraic entropyTopology and its Applications, 159
-
Kaplansky (1954)
Infinite Abelian groups University of Michigan Publications in Mathematics no Arbor University of Michigan PressAnn
-
D. Dikranjan, K. Gong, P. Zanardo (2013)
Endomorphisms of abelian groups with small algebraic entropyLinear Algebra and its Applications, 439
-
J. Peters (1979)
Entropy on discrete abelian groupsAdvances in Mathematics, 33
-
Stojanov (1987)
Uniqueness of topological entropy for endomorphisms on compact groups Boll Un Mat noItal, 7
-
B. Hood (1974)
Topological Entropy and Uniform SpacesJournal of The London Mathematical Society-second Series
-
Smyth (2008)
TheMahler measure of algebraic numbers : a survey Number theory and polynomials Lecture Note Ser Cambridge CambridgeLondonMath Soc Univ
-
Hironaka (2009)
What is Lehmer s number ? Not noAmer Math Soc
-
E. Hewitt, K. Ross (1963)
Abstract Harmonic Analysis -
D. Lind, T. Ward (1988)
Automorphisms of solenoids and p-adic entropyErgodic Theory and Dynamical Systems, 8
-
N. Koblitz (1977)
p-adic numbers -
Victor Snaith (2000)
HEIGHTS OF POLYNOMIALS AND ENTROPY IN ALGEBRAIC DYNAMICS (Universitext) By G RAHAM E VEREST and T HOMAS W ARD : 212 pp., £35.00, ISBN 1 85233 125 9 (Springer, 1999).Bulletin of The London Mathematical Society, 32
-
Fernando Gouvêa (1993)
P-Adic Numbers: An Introduction -
Adler (1965)
Topological entropyTrans Amer Math Soc
-
A. Rotkiewicz, R. Wasén (1980)
Lehmer's numbersActa Arithmetica, 36
-
Dikranjan (2013)
Endomorphisms of Abelian groups with small algebraic entropy Linear noAlgebra Appl
-
D. Dikranjan, B. Goldsmith, L. Salce, P. Zanardo (2009)
ALGEBRAIC ENTROPY FOR ABELIAN GROUPSTransactions of the American Mathematical Society, 361
-
D. Dikranjan, A. Bruno (2012)
Limit free computation of entropyarXiv: Dynamical Systems
-
I. Kaplansky (1954)
Infinite Abelian groups
- Publisher
- de Gruyter
- Copyright
- Copyright © 2015 by the
- ISSN
- 2299-3231
- eISSN
- 2299-3231
- DOI
- 10.1515/taa-2015-0008
- Publisher site
- See Article on Publisher Site
Abstract
Abstract 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.
Journal
Topological Algebra and its Applications – de Gruyter
Published: Nov 26, 2015