Vladimir I. Arnold
Vladimir Igorevich Arnold (1937–2010) was a Soviet and Russian mathematician renowned for foundational work in dynamical systems and mathematical physics, including the Kolmogorov–Arnold–Moser (KAM) theory, singularity theory, symplectic geometry, and catastrophe theory. A prolific author and influential teacher, he shaped modern mathematics through seminal research and widely read expository texts.
Books
This list of books are ONLY the books that have been ranked on the lists that are aggregated on this site. This is not a comprehensive list of all books by this author.
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1. Catastrophe Theory
A concise, rigorous introduction to the mathematics of singularities and bifurcations in smooth systems, developing the classification of elementary catastrophes (fold, cusp, swallowtail, butterfly, and the elliptic, hyperbolic, and parabolic umbilics), the geometry of caustics and wave fronts, and the tools of normal forms, versal deformations, and structural stability. It links these ideas to gradient dynamics and Morse theory, provides illustrative examples from mechanics and optics, and distinguishes solid applications from overextended claims.
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2. Ergodic Problems Of Classical Mechanics
A concise exploration of ergodic phenomena in Hamiltonian dynamics, presenting a curated set of problems and insights on integrability, chaos, and the statistical behavior of classical mechanical systems. It examines geodesic flows, billiard dynamics, and measure-preserving transformations; contrasts KAM stability with mixing and Anosov behavior; and discusses entropy, diffusion, and recurrence on energy surfaces. Emphasizing rigorous questions, examples, and conjectures, it highlights how the topology and geometry of phase space shape long-term dynamics and the foundations of statistical mechanics.