Nice sets and invariant densities in complex dynamics
2010 ◽
Vol 150
(1)
◽
pp. 157-165
◽
Keyword(s):
AbstractIn complex dynamics, we construct a so-called nice set (one for which the first return map is Markov) around any point which is in the Julia set but not in the post-singular set, adapting a construction of Rivera–Letelier. This simplifies the study of absolutely continuous invariant measures. We prove a converse to a recent theorem of Kotus and Świątek, so for a certain class of meromorphic maps the absolutely continuous invariant measure is finite if and only if an integrability condition is satisfied.
1987 ◽
Vol 30
(3)
◽
pp. 301-308
◽
2008 ◽
Vol 145
(3)
◽
pp. 685-697
◽
2013 ◽
Vol 23
(05)
◽
pp. 1350079
2012 ◽
Vol 396
(1)
◽
pp. 1-6
1993 ◽
Vol 03
(04)
◽
pp. 1045-1049
1996 ◽
Vol 06
(06)
◽
pp. 1143-1151
2012 ◽
Vol 33
(2)
◽
pp. 529-548
◽