Measure of parameters with a.c.i.m. nonadjacent to the Chebyshev value in the quadratic family

Loading...
Thumbnail Image

Files

Publication or External Link

Date

2012

Citation

DRUM DOI

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.

Notes

Rights