Regular and stochastic dynamics in the real quadratic family

  1. Mikhail Lyubich
  1. Institute for Mathematical Sciences, State University of New York, Stony Brook, NY 11794

  1. Communicated by John W. Milnor, State University of New York, Stony Brook, NY (received for review July 26, 1998)

Abstract

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

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  1. PNAS November 24, 1998 vol. 95 no. 24 14025-14027
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