  For an arbitrary topological group G any compact G-dynamical system (G,X) can
be linearly G-represented as a weak*-compact subset of a dual Banach space V*.
As was shown by Megrelishvili (2003), the Banach space V can be chosen to be
reflexive iff the metric system (G,X) is weakly almost periodic (WAP). In this
paper we study the wider class of compact G-systems which can be linearly
represented as a weak*-compact subset of a dual Banach space with the
Radon-Nikodym property. We call such a system a Radon-Nikodym system (RN). One
of our main results is to show that for metrizable compact G-systems the three
classes: RN, HNS (hereditarily not sensitive) and HAE (hereditarily almost
equicontinuous) coincide. We investigate these classes and their relation to
previously studied classes of G-systems such as WAP and LE (locally
equicontinuous). We show that the Glasner-Weiss examples of
recurrent-transitive locally equicontinuous but not weakly almost periodic
cascades are actually RN. We also show that for symbolic systems the RN
property is equivalent to having a countable phase space; and that any
Z-dynamical system (f,X), where X is either the unit interval or the unit
circle and f: X\to X is a homeomorphism, is an RN system. Using fragmentability
and Namioka's theorem we give an enveloping semigroup characterization of HNS
systems and show that the enveloping semigroup of a compact metrizable HNS
system is a separable Rosenthal compact, hence of cardinality less than or
equal c. We investigate a dynamical version of the Bourgain-Fremlin-Talagrand
dichotomy and a dynamical version of Todor\u{c}evi\'{c} dichotomy concerning
Rosenthal compacts.
