Tomas Johnson: Oscillatory motion for the universal area-preserving map associated with period doubling

The detection of oscillatory motion, i.e., orbits that approach infinity and then return to a bounded domain, is important for many applications, e.g., in celestial mechanics. During this talk I will describe how to use the area- preserving period doubling renormalization operator to construct oscillating orbits for the universal area- preserving map associated with period doubling. The construction uses two ingredients in an essential way: a computational shadowing technique called covering relations, and the invariance of the map under period doubling.

This is joint work with Denis Gaidashev (Uppsala).