2018/09/09 by Mauricio Garay, Garay, Mauricio, Duco van Straten +1
Mathematics · #70H08 and 37J40 #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1809.03492
openalex publication_date 2018/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is part II of our book on KAM theory. We start by defining functorial analysis and then switch to the particular case of Kolmogorov spaces. We develop functional calculus based on the notion of local operators. This allows to define the exponential and therefore relation between Lie algebra and Lie group actions in the infinite dimensional context. Then we introduce a notion of finite dimensional reduction and use it to prove a fixed point theorem for Kolmogorov spaces. We conclude by proving general normal theorems.