Contributed Session 1:  ODEs and Applications
The formal ultra-differential normalization for random dynamical systems
Weifang Hu
School of Mathematics, Southeast University
Peoples Rep of China
  Co-Author(s):    Hao Wu
  Abstract:
 

We present a framework for establishing ultradifferential normal forms on various tempered neighborhoods for random dynamical systems. More precisely, we provide sharper estimates of the loss of ultra-differential smoothness by small divisor conditions, tempered neighborhood, and the order of non-resonant terms based on the Lyapunov exponents of linear parts. The tools utilised here are ergodic theorems and fixed point theorems on weighted Banach spaces.