In the early development of complex dynamics in dimension one, made heavy use was made of Montel's Theorem.
In fact, much of the theory may be obtained directly from Montel's Theorem (which says that any family of
holomorphic mappings from the disk into *C* minus 2 points is a normal family). There are
generalizations of Montel's Theorem to higher dimension, but it is not clear how these can be applied to
obtain the analogous theorems in higher-dimensionaldynamics.

Fortunately, pluri-potential theory has been applicable as an alternative tool. This approach to dynamics
focuses more on measurable dynamics and ergodic theory.
By "pluri-potential" theory, we
mean the theory of pluri-subharmonic (psh) functions and positive, closed currents. With this, we can
define the stable/unstable currents. Further, the
operator *(dd ^{c})^{2}* has been useful for defining the wedge (intersection) product
of these two currents.
An early presentation of

One of my favorite results involving pluri-potential theory is:

**Theorem** [Fornaess and Sibony] *If T is a positive, closed current whose support
is contained in K^{+},
*

then T is a positive multiple of the stable current.

This has been generalized recently in a very nice paper by Dinh and Sibony. Look at this paper also for a nice exposition of many aspects of pluri-potential theory.

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