Renormalization: Masur and Veech solution to Keane conjecture. Moreira-Yoccoz solution to Palis conjecture
By Carlos Matheus
By Richard-Evan Schwartz
By Katrin Gelfert
By De-Jun Feng
Traditionally homogenization asks whether average behavior can be discerned from Hamilton-Jacobi equations that are subject to high-frequency fluctuations in spatial variables. A similar question can be asked for the associated Hamiltonian ODEs. When the Hamiltonian function is convex in momentum variable, these two questions turn out to be equivalent. This equivalence breaks down for general Hamiltonian functions. In this talk I will give a dynamical system formulation for homogenization and address some result concerning weak and strong homogenization phenomena.