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Asymptotical behavior of piecewise contractions of the interval.

Friday 20th June 2014 - 14:30 to 15:30
INI Seminar Room 2
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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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons