In 1990s Bruin, Keller, Nowicki, and van Strien showed that smooth unimodal maps with Fibonacci combinatorics and sufficiently high degree of a critical point have a wild attractor, i.e. their metric and topological attractors do not coincide. However, until now there were no reasonable estimates on the degree of the critical point needed. In the talk I will present an approach for studying attractors of maps, which are periodic points of a renormalization. Using this approach and rigorous computer estimates, we show that the Fibonacci map of degree d=3.8 does not have a wild attractor, but that for degree d=5.1 the wild attractor exists.
The talk is based on a joint work with Denis Gaidashev.
Meeting ID: 852 4277 3200 Passcode: 103121