Regular and stochastic dynamics in the real quadratic family.

Lyubich, M · Proc Natl Acad Sci U S A · 1998

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Abstract

We prove the Regulat or Stochastic Conjecture for the real quadratic family which asserts that almost every real quadratic map Pc, c in [-2, 1/4], has either an attracting cycle or an absolutely continuous invariant measure.