Abstract:
In this paper we present the concepts of Baire Ergodicity and Ergodic Formalism introduced in \cite{Pi1}.
We use them to study topological attractors and statistical attractors and, in particular, to determine their existence and finiteness.
These concepts are also used to investigate topological attractors of interval maps, even with discontinuities.
To do this, we analyze the attractors of wandering intervals. As a result, we demonstrate the finiteness of non-periodic attractors of $C^2$ applications with discontinuities.
For applications of the interval $C^2$ without discontinuities, we show that the topological and statistical attractors coincide and we calculate the Birkhoff upper mean of continuous functions for generic points.
