Fixed point theorems for small divisors problems

2025/04/28 by Garay, Mauricio, van Straten, Duco
#47J07 #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2504.19808

Abstract

In the seventies', Zehnder found a Nash-Moser type implicit function theorem in the analytic set-up. This theorem has found many applications in dynamical systems although its applications require, as a general rule, some efforts. We develop further the analytic theory and give fixed point theorems with direct applications to the study of dynamical systems.

Citations

• KAM via Standard Fixed Point Theorems
• A Category of Banach Space Functors
• The Herman invariant tori conjecture
• Quasi-periodic motions on symplectic tori
• An abstract KAM theorem
• A proof of the invariant torus theorem of Kolmogorov
• Un théorème de fonctions implicites sur certains espaces de Fréchet et quelques applications

Related

• An Introduction To Small Divisors
• Small Divisor problems and A_p weights with an application
• Some open problems in low dimensional dynamical systems
• Nash--Moser iteration and singular perturbations
• Fixed Point Theory: A Review