Table of Contents

Chapter 1 . Basic Concepts

Chapter 2 . Basic Theorems

Chapter 3 . Linear Systems

Chapter 4 . Proofs of the Main Theorems

Chapter 5 . Differential Equations On Manifolds

About the Author

Vladimir I. Arnold was a Soviet and Russian mathematician. He is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, and contributed to several areas, including geometrical theory of dynamical systems theory, algebra, catastrophe theory, topology, real algebraic geometry, symplectic geometry, symplectic topology, differential equations, classical mechanics, differential geometric approach to hydrodynamics, geometric analysis and singularity theory, including posing the ADE classification problem.

His first main result was the solution of Hilbert's thirteenth problem in 1957 at the age of 19. He co-founded three new branches of mathematics: topological Galois theory (with his student Askold Khovanskii), symplectic topology and KAM theory.

Arnold was also known as a popularizer of mathematics. Through his lectures, seminars, and as the author of several textbooks (such as Mathematical Methods of Classical Mechanics) and popular mathematics books, he influenced many mathematicians and physicists.[5][6] Many of his books were translated into English. His views on education were particularly opposed to those of Bourbaki.