BROWNIAN-MOTION AND THE EQUILIBRIUM MEASURE ON THE JULIA SET OF A RATIONAL MAPPING
成果类型：
Article
署名作者：
LALLEY, SP
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176989536
发表日期：
1992
页码：
1932-1967
关键词：
摘要：
It is proved that if a rational mapping has infinity as a fixed point in its Fatou set, then its Julia set has positive capacity and the equilibrium measure is invariant. If infinity is attracting or superattracting, then the equilibrium measure is strongly mixing, whereas if infinity is neutral, then the equilibrium measure is ergodic and has entropy zero. Lower bounds for the entropy are given in the attracting and superattracting cases. If the Julia set is totally disconnected, then the equilibrium measure is Gibbs and therefore Bernoulli. The proofs use an induced action by the rational mapping on the space of Brownian paths started at infinity.
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