We consider perturbations of interval maps with indifferent fixed points, which we refer to as wobbly interval intermittent maps, for which stable laws for general Hölder observables fail. We obtain limit laws for such maps and Hölder observables. These limit laws are similar to the classical semistable laws previously established for random processes. One of the examples considered is an interval map with a countable number of discontinuities, and to analyse it we need to construct a Markov/Young tower.

We study a class of one-dimensional full branch maps admitting two indifferent fixed points as well as critical points and/or unbounded derivative. Under some mild assumptions we prove the existence of a unique invariant mixing absolutely continuous probability measure, study its rate of decay of correlation and prove a number of limit theorems.

We consider perturbations of interval maps with indifferent fixed points, which we refer to as wobbly interval intermittent maps, for which stable laws for general Hölder observables fail. We obtain limit laws for such maps and Hölder observables. These limit laws are similar to the classical semistable laws previously established for deterministic processes, but certain limitations imposed by the current dynamical setup are reflected in the main result. One of the considered examples is an interval map with a countable number of discontinuities, and to analyse it we need to construct a Markov/Young tower.