Nonuniformly expanding 1d maps with logarithmic singularities
  For a certain parametrized family of maps on the circle with critical points and logarithmic singularities where derivatives blow up to infinity, we construct a positive measure set of parameters corresponding to maps which exhibit nonuniformly expanding behavior. This implies the existence of "chaotic" dynamics in dissipative homoclinic tangles in periodically perturbed differential equations. 
Hiroki Takahasi and Qiudong Wang
math.DS