Abundance of Wild Historic Behavior

摘要

Using Caratheodory measures, we associate to each positive orbit O-f(+)(x) of a measurable map f, a Borel measure eta(x). We show that eta(x) is f-invariant whenever f is continuous or eta(x) is a probability. These measures are used to study the historic points of the system, that is, points with no Birkhoff averages, and we construct topologically generic subset of wild historic points for wide classes of dynamical models. We use properties of the measure eta(x) to deduce some features of the dynamical system involved, like the existence of heteroclinic connections from the existence of open sets of historic points.