Highly Influenced

# Almost Every Real Quadratic Map Is Either Regular or Stochastic

@inproceedings{Lyubich1997AlmostER, title={Almost Every Real Quadratic Map Is Either Regular or Stochastic}, author={Mikhail Lyubich}, year={1997} }

- Published 1997

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 P c : x → 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.

Highly Cited

This paper has 56 citations. REVIEW CITATIONS

#### From This Paper

##### Topics from this paper.

#### Citations

##### Publications citing this paper.

#### Citation Statistics

#### 57 Citations

Citations per Year

Semantic Scholar estimates that this publication has

**57**citations based on the available data.See our **FAQ** for additional information.