Abstract:
 The Sunimodal maps is a class of onedimensional maps that is well studied.
In these talks,I will introduce some basic properties of Sunimodal maps, and look at the characterization of such maps. We will see the properties present through the family of quadratic maps $f_\lambda(x) =\lambda_x(1  x)
$ with parameter $\lambda$ ranging from 0 to 4. Then we look at some properties of the parameter space of this given family. For certain parameters, there exist absolutely continuous invariant measures. We look at
sufficient conditions for existence of absolutely continuous invariant measures. Finally, we study ergodic properties of these absolutely continuous invariant measures.
