# Asymptotical behavior of piecewise contractions of the interval.

Presented by:
A Nogueira Aix Marseille Université
Date:
Friday 20th June 2014 - 14:30 to 15:30
Venue:
INI Seminar Room 2
Abstract:
A map $f:[0,1)\to [0,1)$ is a piecewise contraction of $n$ intervals, if there exists a partition of $[0,1)$ into intervals $I_1, \ldots, I_n$ and every restriction $f\vert_{I_i}$ is an injective Lipschitz contraction. Among other results we will show that a typical piecewise contraction of $n$ intervals has at least one and at most $n$ periodic orbits. Moreover, for every point $x$, the $\omega$-limit set of $x$ equals a periodic orbit.

The talk is based in a joint work with B. Pires and R. Rosales.

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.