• DOI:10.1007/BF01941800
Corpus ID: 119956479

Absolutely continuous invariant measures for one-parameter families of one-dimensional maps

@article{Jakobson1981AbsolutelyCI,
  title={Absolutely continuous invariant measures for one-parameter families of one-dimensional maps},
  author={M. Jakobson},
  journal={Communications in Mathematical Physics},
  year={1981},
  volume={81},
  pages={39-88}
}

M. Jakobson

Published 1981

Mathematics

Communications in Mathematical Physics

View on Springer

Save to Library

Create Alert

Cite

Launch Research Feed

Given a one-parameter familyfλ(x) of maps of the interval [0, 1], we consider the set of parameter values λ for whichfλ has an invariant measure absolutely continuous with respect to Lebesgue measure. We show that this set has positive measure, for two classes of maps: i)fλ(x)=λf(x) where 0<λ≦4 andf(x) is a functionC3-near the quadratic mapx(1−x), and ii)fλ(x)=λf(x) (mod 1) wheref isC3,f(0)=f(1)=0 andf has a unique nondegenerate critical point in [0, 1].