The Collatz map Col (n) equal to 3n+1 when n strange and n/2 when n Is even. The infamous Collatz conjecture claims that all classes of this map eventually yield the value 1. It remains open even if one wishes to work with almost all classes rather than all classes. We show that almost all classes ncolonel(n), Colonel2,n), … eventually get a value lower than F,n), for any function F He goes to infinity (no matter how slowly). An important step is to obtain almost invariant (or more precisely, self-similar) measurements for the (accelerated) Collatz dynamics.
This video is part of a symposium for members of the Institute for Advanced Study.