TY - JOUR
T1 - Sharing a Measure of Maximal Entropy in Polynomial Semigroups
AU - Pakovich, Fedor
N1 - Publisher Copyright:
© The Author(s) 2021. Published by Oxford University Press. All rights reserved.
PY - 2022/9/1
Y1 - 2022/9/1
N2 - Let P1, P2, . . . , Pk be complex polynomials of degree at least two that are not simultaneously conjugate to monomials or to Chebyshev polynomials, and S the semigroup under composition generated by P1, P2, . . . , Pk. We show that all elements of S share a measure of maximal entropy if and only if the intersection of principal left ideals SP1 ∩ SP2 ∩ · · · ∩ SPk is non-empty.
AB - Let P1, P2, . . . , Pk be complex polynomials of degree at least two that are not simultaneously conjugate to monomials or to Chebyshev polynomials, and S the semigroup under composition generated by P1, P2, . . . , Pk. We show that all elements of S share a measure of maximal entropy if and only if the intersection of principal left ideals SP1 ∩ SP2 ∩ · · · ∩ SPk is non-empty.
UR - http://www.scopus.com/inward/record.url?scp=85110986292&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnab076
DO - 10.1093/imrn/rnab076
M3 - Article
AN - SCOPUS:85110986292
SN - 1073-7928
VL - 2022
SP - 13829
EP - 13840
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 18
ER -