Dissertation/Thesis Abstract

Measure of parameters with a.c.i.m. nonadjacent to the Chebyshev value in the quadratic family
by Huang, Yu-Ru, Ph.D., University of Maryland, College Park, 2012, 192; 3517679
Abstract (Summary)

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.

Indexing (document details)
Advisor: Jakobson, Michael
Commitee: Boyle, Mike, Dolgopyat, Dmitry, Forni, Giovanni, Purtilo, Jim
School: University of Maryland, College Park
Department: Mathematics
School Location: United States -- Maryland
Source: DAI-B 73/12(E), Dissertation Abstracts International
Source Type: DISSERTATION
Subjects: Mathematics
Keywords: Absolutely continuous invariant measures, Chebyshev value, Quadratic family
Publication Number: 3517679
ISBN: 978-1-267-48101-6
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