Title : Piecewise contractions are typically asymptotically periodic
Speaker: Henk Bruin
Affiliation: University of Vienna
Time: 11 am Friday, 8 January, 2016
Location: 303-412
A piecewise contraction is defined on a finite partition of a metric phase space (X,d). Each partition element is mapped by a contraction into X. Since the contraction is only piecewise, it is not a priori clear (and true) that orbits are attracted to periodic orbits. However, in joint work with Jonathan Deane (University of Surrey), we prove that for parametrized families of planar piecewise contractions, typically all orbits are asymptotically periodic. The method can be extended to higher dimension and systems with varying partitions as well.

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