Almost Every Real Quadratic Map Is Either Regular or Stochastic
نویسنده
چکیده
Stony Brook IMS Preprint #1997/8 July, 1997 Abstract. We prove uniform hyperbolicity of the renormalization operator for all possible real combinatorial types. We derive from it that the set of infinitely renormalizable parameter values in the real quadratic family Pc : x 7→ x 2 + c has zero measure. This yields the statement in the title (where “ regular” means to have an attracting cycle and “stochastic” means to have an absolutely continuous invariant measure). An application to the MLC problem is given.
منابع مشابه
Regular and stochastic dynamics in the real quadratic family.
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.
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تاریخ انتشار 1997