Semistable laws for wobbly intermittent maps
Ergodic Theory and Dynamical Systems Seminar
13th June 2019, 2:00 pm – 3:00 pm
Howard House, 4th Floor Seminar Room
For the LSV map with parameter ½ < γ < 1 S. Gouëzel has shown that Hölder observables v that "see" the neutral fixed point, v(0) ≠ 0, will satisfy a stable law. A key property that allows Gouëzel to establish this result is the fact that the return time of the LSV map to the right half of the unit interval has a regularly varying tail distribution. I will present ongoing work joint with M. Holland and D. Terhesiu in which we study "wobbly" intermittent interval maps where this regular variation is not present in the tail of the return time. In this setting we show that for a wide class of oberservables the stable laws of Gouëzel break down and semistable laws appear.