Nice sets and invariant densities in complex dynamics

作者：Dobbs Neil^*

来源：Mathematical Proceedings of the Cambridge Philosophical Society, 2011, 150: 157-165.

DOI：10.1017/S0305004110000265

In 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 'Swiatek, so for a certain class of meromorphic maps the absolutely continuous invariant measure is finite if and only if an integrability condition is satisfied.

• 出版日期2011-1