Thursday 14 Feb 2019: Pure/Dynamics Seminar: Coexistence phenomena for dissipative maps
Michael Benedicks -
The first main result is that for the classical Hénon maps, and for each integer k=1,2,..., there exists a set of parameters of positive two-dimensional Lebesgue measure, such that there are simultaneously at least k distinct attractive periodic orbits and a strange attractor. The method also leads to new constructive proof of the existence of parameters with infinitely many attractive periodic orbits, the so called Newhouse phenomenon. (Joint work with Liviana Palmisano.)
Finally a further set of results concerning the structure of the parameter set of certain dissipative maps with the Newhouse phenomenon is described (joint work with Marco Martens and Liviana Palmisano).