an:03881517
Zbl 0553.58008
Rees, Mary
Ergodic rational maps with dense critical point forward orbit
EN
Ergodic Theory Dyn. Syst. 4, 311-322 (1984).
00148896
1984
j
58E05 37A99 37G99
rational map; Julia set; ergodic; critical point
A proof is given of the fact that a rational map with all critical points eventually mapping to expanding periodic orbits is ergodic with respect to Lebesgue measure. It is shown that in many smooth families of rational maps, if A is the set of functions with all critical points eventually periodic, then \(\bar A\) is uncountable, and contains functions which are ergodic with respect to Lebesgue measure and have dense critical point forward orbit.