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On Finite Blaschke Products whose Restrictions to the unit circle are Exact Endomorphisms
Author(s) -
Martin N. F. G.
Publication year - 1983
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/15.4.343
Subject(s) - mathematics , endomorphism , unit circle , blaschke product , cartesian product , lebesgue measure , unit disk , pure mathematics , mathematical analysis , lebesgue integration , discrete mathematics
An easily checked sufficient condition is given for the restriction of a finite Blaschke product to the unit circle to be an exact endomorphism. A formula for the entropy of such restrictions with respect to the unique finite invariant measure equivalent to Lebesgue measure is given and it is shown that if such a restriction has maximal entropy then it is conformally equivalent to the product of a rotation and a power.