Positive Lyapunov exponent for generic one-parameter families of unimodal maps

@article{Thieullen1994PositiveLE,
  title={Positive Lyapunov exponent for generic one-parameter families of unimodal maps},
  author={Ph. Thieullen and C. Tresser and Lai-Sang Young},
  journal={Journal d’Analyse Math{\'e}matique},
  year={1994},
  volume={64},
  pages={121-172}
}
AbstractLetfaa∈A be a C2 one-parameter family of non-flat unimodal maps of an interval into itself anda* a parameter value such that(a)fa* satisfies the Misiurewicz Condition,(b)fa* satisfies a backward Collet-Eckmann-like condition,(c)the partial derivatives with respect tox anda of fan(x), respectively at the critical value and ata*, are comparable for largen. Thena* is a Lebesgue density point of the set of parameter valuesa such that the Lyapunov exponent of fa at the critical value is… CONTINUE READING