Expanding interval maps with intermittent behaviour, physical measures and time scales (Q1884231)

A construction leading to a family of piecewise monotonic expanding interval maps with interesting intermittent behavior is given. There are examples with an indifferent fixed-point and infinite absolutely continuous invariant measure. Here, the Dirac mass at 0 describes the statistical behavior at usual time scale while the infinite one tells about statistical behavior at larger scales. There is another invariant measure describing the statistical behavior at a third natural time scale. Finally, a construction leading to an example with expected infinite number of time scales is proposed.