TY - JOUR
T1 - When do two rational functions have the same Julia set?
AU - Levin, G.
AU - Przytycki, And F.
PY - 1997
Y1 - 1997
N2 - It is proved that non-exceptional rational functions f and g on the Riemann sphere have the same measure of maximal entropy iff there exist iterates F of f and G of g and natural numbers M, N such that (*) (G-1 o G) o GM= (F-1 o F) o FN. If one assumes only that f, g have the same Julia set and no singular or parabolic domains of normality for the iterates, one also proves (*).
AB - It is proved that non-exceptional rational functions f and g on the Riemann sphere have the same measure of maximal entropy iff there exist iterates F of f and G of g and natural numbers M, N such that (*) (G-1 o G) o GM= (F-1 o F) o FN. If one assumes only that f, g have the same Julia set and no singular or parabolic domains of normality for the iterates, one also proves (*).
UR - http://www.scopus.com/inward/record.url?scp=21744459806&partnerID=8YFLogxK
U2 - 10.1090/s0002-9939-97-03810-0
DO - 10.1090/s0002-9939-97-03810-0
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AN - SCOPUS:21744459806
SN - 0002-9939
VL - 125
SP - 2179
EP - 2190
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 7
ER -