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Law of iterated logarithm and invariance principle for one-parameter families of interval maps
Daniel Schnellmann
We show that for almost every map in a transversal one-parameter family of piecewise expanding unimodal maps the Birkhoff sum of suitable observables along the forward orbit of the…
Whitney-Holder continuity of the SRB measure for transversal families of smooth unimodal maps
Viviane Baladi, Michael Benedicks, Daniel Schnellmann
We consider C^2 families t->f_t of C^4 nondegenerate unimodal maps. We study the absolutely continuous invariant probability (SRB) measure m_t of f_t, as a function of t on the set…
Ergodic properties of Viana-like maps with singularities in the base dynamics
José Ferreira Alves, Daniel Schnellmann
We consider two examples of Viana maps for which the base dynamics has singularities (discontinuities or critical points) and show the existence of a unique absolutely continuous i…
Typical points for one-parameter families of piecewise expanding maps of the interval
Daniel Schnellmann
Let be an interval and , , a one-parameter family of piecewise expanding maps such that for each the map admits a uni…