On geometric methods in works by V.I.Arnold and V.V.Kozlov

TL;DR

This paper surveys geometric methods employed by Arnold and Kozlov, focusing on normal forms, polyhedra, small denominators, and asymptotic expansions, highlighting their applications in mathematical physics and dynamical systems.

Contribution

It provides a comprehensive overview of the geometric techniques used by Arnold and Kozlov, emphasizing their differences and applications in various mathematical contexts.

Findings

Comparison of methods used by Arnold and Kozlov

Summary of geometric techniques like normal forms and polyhedra

Insights into applications of small denominators and asymptotic expansions

Abstract

We give a survey of geometric methods used in papers and books by V.I.Arnold and by V.V.Kozlov. They are methods of different normal forms, of different polyhedra, of small denominators and of asymptotic expansions.