TY - JOUR
T1 - Sharing a Measure of Maximal Entropy in Polynomial Semigroups
AU - Pakovich, Fedor
N1 - rnab076
PY - 2021/5/1
Y1 - 2021/5/1
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\cap SP2\cap \dots \cap 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\cap SP2\cap \dots \cap SPk\ is non-empty.
U2 - https://doi.org/10.1093/imrn/rnab076
DO - https://doi.org/10.1093/imrn/rnab076
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
SN - 1073-7928
IS - rnab076
ER -