TY - JOUR
T1 - Entropy for endomorphisms of LCA groups
AU - Virili, Simone
PY - 2012/6/1
Y1 - 2012/6/1
N2 - We introduce a modified version of the entropy defined for locally compact Abelian groups by Peters. This approach allows us to work with endomorphisms instead of working with automorphisms. We study some of the basic properties of this new entropy and we give direct proofs of the formulae that allow one to compute the entropy of endomorphisms of Z{double-struck} N, R{double-struck} N and C{double-struck} N, for every positive integer N. © 2012 Elsevier B.V.
AB - We introduce a modified version of the entropy defined for locally compact Abelian groups by Peters. This approach allows us to work with endomorphisms instead of working with automorphisms. We study some of the basic properties of this new entropy and we give direct proofs of the formulae that allow one to compute the entropy of endomorphisms of Z{double-struck} N, R{double-struck} N and C{double-struck} N, for every positive integer N. © 2012 Elsevier B.V.
KW - Algebraic entropy
KW - Continuous endomorphisms
KW - Haar measure
KW - Locally compact abelian groups
UR - https://www.scopus.com/pages/publications/84860842021
U2 - 10.1016/j.topol.2011.02.017
DO - 10.1016/j.topol.2011.02.017
M3 - Article
SN - 0166-8641
VL - 159
SP - 2546
EP - 2556
JO - Topology and its Applications
JF - Topology and its Applications
IS - 9
ER -