# GAN

## Seminar

### Asymptotical behavior of piecewise contractions of the interval.

Seminar Room 2, Newton Institute Gatehouse

#### 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.

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