The absolute continuity of the invariant measure of random iterated function systems with overlaps

Balazs Bárány, Tomas Persson

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Sammanfattning

We consider iterated function systems on the interval with random perturbation. Let Yε be uniformly distributed in [1−ε, 1+ε] and let fi ∈ C 1+α be contractions with fixpoints ai . We consider the iterated function system {Yε fi + ai (1 − Yε )}, where each of the maps is chosen with probability pi . It is shown that the invariant density is in L2 and its L2 norm does not grow faster than 1/√ε as ε vanishes.
The proof relies on defining a piecewise hyperbolic dynamical system on the cube with
an SRB-measure whose projection is the density of the iterated function system.
Originalspråkengelska
Sidor (från-till)47-62
TidskriftFundamenta Mathematicae
Volym210
Utgåva1
DOI
StatusPublished - 2010

Ämnesklassifikation (UKÄ)

  • Matematik

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