Measure of parameters with a.c.i.m. nonadjacent to the Chebyshev value in the quadratic family
| dc.contributor.advisor | Jakobson, Michael | en_US |
| dc.contributor.author | Huang, Yu-Ru | en_US |
| dc.contributor.department | Mathematics | en_US |
| dc.contributor.publisher | Digital Repository at the University of Maryland | en_US |
| dc.contributor.publisher | University of Maryland (College Park, Md.) | en_US |
| dc.date.accessioned | 2012-07-07T06:12:49Z | |
| dc.date.available | 2012-07-07T06:12:49Z | |
| dc.date.issued | 2012 | en_US |
| dc.description.abstract | In this thesis, we consider the quadratic family f_t(x)=tx(1-x), and the set of parameter values t for which f_t has an absolutely continuous invariant measures (a.c.i.m.). It was proven by Jakobson that the set of parameter values t for which f_t 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 f_t has an a.c.i.m. in that interval. | en_US |
| dc.identifier.uri | http://hdl.handle.net/1903/12731 | |
| dc.subject.pqcontrolled | Mathematics | en_US |
| dc.title | Measure of parameters with a.c.i.m. nonadjacent to the Chebyshev value in the quadratic family | en_US |
| dc.type | Dissertation | en_US |
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