  A relevant problem in dynamics is to characterize how deterministic systems
may exhibit features typically associated to stochastic processes. A widely
studied example is the study of (normal or anomalous) transport properties for
deterministic systems on a non-compact phase space. We consider here two
examples of area-preserving maps: the Chirikov-Taylor standard map and the
Casati-Prosen triangle map, and we investigate transport properties, records'
statistics and occupation time statistics. While the standard map, when a
chaotic sea is present, always reproduces results expected for simple random
walks, the triangle map -- whose analysis still displays many elusive points --
behaves in a wildly different way, some of the features being compatible with a
transient (non conservative) nature of the dynamics.
