Absolutely continuous invariant measures for piecewise linear interval maps both expanding and contracting

• Main Author: Islam, Md. Shafiqul
• Format: Others
• Published: 2000
• Online Access: http://spectrum.library.concordia.ca/1181/1/MQ54294.pdf; Islam, Md. Shafiqul <http://spectrum.library.concordia.ca/view/creators/Islam=3AMd=2E_Shafiqul=3A=3A.html> (2000) Absolutely continuous invariant measures for piecewise linear interval maps both expanding and contracting. Masters thesis, Concordia University.

Let [Special characters omitted.] be a family of piecewise linear maps f : [-1,1] [arrow right] [-1,1] with a discontinuity at x = 0 such that f is expanding in one of the intervals (-1,0), (0,1) and contracting in the other. We will study the dynamics of maps of sub-classes of [Special characters omitted.] . It will be shown that a map in such a sub-class of [Special characters omitted.] either has a periodic attractor or is eventually expanding. In the latter case, there exists an absolutely continuous invariant measure (acim) and in many examples we will find the measure.