Vladimir Arnold is one of the greatest mathematical scientists of our time, as well as one of the finest, most prolific mathematical authors. This first volume of his Collected Works focuses on representations of functions, celestial mechanics and KAM theory.

Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry.

Vladimir Arnold is one of the most outstanding mathematicians of our time Many of these problems are at the front line of current research

This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

The first complete proof of Arnold diffusion—one of the most important problems in dynamical systems and mathematical physics Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted the efforts of some of the most prominent researchers in mathematics. The question is whether a typical perturbation of a particular system will result in chaotic or unstable dynamical phenomena. In this groundbreaking book, Vadim Kaloshin and Ke Zhang provide the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five-dimensional integrable systems (two and a half degrees of freedom). This proof realizes a plan John Mather announced in 2003 but was unable to complete before his death. Kaloshin and Zhang follow Mather's strategy but emphasize a more Hamiltonian approach, tying together normal forms theory, hyperbolic theory, Mather theory, and weak KAM theory. Offering a complete, clean, and modern explanation of the steps involved in the proof, and a clear account of background material, this book is designed to be accessible to students as well as researchers. The result is a critical contribution to mathematical physics and dynamical systems, especially Hamiltonian systems.

'EMS 6' is the latest volume in the sub series 'Dynamical Systems of the Encyclopaedia'. It is the first of two volumes covering Singularity Theory, which, besides its fundamental use in Dynamical Systems and Bifurcation Theory, is an important part of other fields such as algebraic geometry, differential geometry and geometric optics.

This is a charming collection of essays on life and science, by one of the leading mathematicians of our day. Vladimir Igorevich Arnold is renowned for his achievements in mathematics, and nearly as famous for his informal teaching style, and for the clarity and accessibility of his writing. The chapter headings convey Arnold’s humor and restless imagination. A few examples: My first recollections; The combinatorics of Plutarch; The topology of surfaces according to Alexander of Macedon; Catching a pike in Cambridge. Yesterday and Long Ago offers a rare opportunity to appreciate the life and work of one of the world’s outstanding living mathematicians.