In this thesis, we consider the quadratic family ft( x)=tx(1−x), and the set of parameter values t for which ft has an absolutely continuous invariant measures (a.c.i.m.). It was proven by Jakobson that the set of parameter values t for which ft has an a.c.i.m. has positive Lebesgue measure. Most of the known results about the existence and the measure of parameter values with a.c.i.m. concern a small neighborhood of the Chebyshev parameter value t=4. Differently from previous works, we consider an interval of parameter not adjacent to t=4, and give a lower bound for the measure of the set of parameter values t for which ft has an a.c.i.m. in that interval.
|Commitee:||Boyle, Mike, Dolgopyat, Dmitry, Forni, Giovanni, Purtilo, Jim|
|School:||University of Maryland, College Park|
|School Location:||United States -- Maryland|
|Source:||DAI-B 73/12(E), Dissertation Abstracts International|
|Keywords:||Absolutely continuous invariant measures, Chebyshev value, Quadratic family|
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