On the asymptotic properties of piecewise contracting maps

@article{Catsigeras2011OnTA,
  title={On the asymptotic properties of piecewise contracting maps},
  author={Eleonora Catsigeras and Pierre Guiraud and Arnaud Meyroneinc and Edgardo Ugalde},
  journal={Dynamical Systems},
  year={2011},
  volume={31},
  pages={107 - 135}
}
ABSTRACT We are interested in the phenomenology of the asymptotic dynamics of piecewise contracting maps. We consider a wide class of such maps and we give sufficient conditions to ensure some general basic properties, such as the periodicity, the total disconnectedness or the zero Lebesgue measure of the attractor. These conditions show in particular that a non-periodic attractor necessarily contains discontinuities of the map. Under this hypothesis, we obtain numerous examples of attractors… 
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