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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.

Bifurcation theory. --- Hydrodynamics. --- Mathematicians -- Biography. --- Mathematicians. --- Mathematics. --- Algebraic geometry. --- Mathematical physics. --- Physics. --- Mathematical Applications in the Physical Sciences. --- Algebraic Geometry. --- Mathematical Methods in Physics. --- Fluid dynamics --- Differential equations, Nonlinear --- Stability --- Numerical solutions --- Geometry, algebraic. --- Algebraic geometry --- Geometry --- Physical mathematics --- Physics --- Mathematics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Geometry, Algebraic.

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First published in 1998 this unique monograph treats topological, group-theoretic, and geometric problems of ideal hydrodynamics and magneto-hydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. This book, now accepted as one of the main references in the field, is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry. The updated second edition also contains a survey of recent developments in this now-flourishing field of topological and geometric hydrodynamics.

Discrete mathematics --- Mathematics --- Classical mechanics. Field theory --- Fluid mechanics --- Statistical physics --- Artificial intelligence. Robotics. Simulation. Graphics --- neuronale netwerken --- fuzzy logic --- cybernetica --- grafentheorie --- statistiek --- systeemtheorie --- wiskunde --- KI (kunstmatige intelligentie) --- ingenieurswetenschappen --- fysica --- dynamica --- vloeistoffen --- AI (artificiële intelligentie)

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Discrete mathematics --- Mathematics --- Classical mechanics. Field theory --- Fluid mechanics --- Statistical physics --- Artificial intelligence. Robotics. Simulation. Graphics --- neuronale netwerken --- fuzzy logic --- cybernetica --- grafentheorie --- statistiek --- systeemtheorie --- wiskunde --- KI (kunstmatige intelligentie) --- ingenieurswetenschappen --- fysica --- dynamica --- vloeistoffen

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Ergodic theory. Information theory --- Partial differential equations --- Differential equations --- Mathematical physics --- differentiaalvergelijkingen --- wiskunde --- fysica --- informatietheorie

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Vladimir Igorevich Arnold is one of the most influential mathematicians of our time. V. I. Arnold launched several mathematical domains (such as modern geometric mechanics, symplectic topology, and topological fluid dynamics) and contributed, in a fundamental way, to the foundations and methods in many subjects, from ordinary differential equations and celestial mechanics to singularity theory and real algebraic geometry. Even a quick look at a partial list of notions named after Arnold already gives an overview of the variety of such theories and domains: KAM (Kolmogorov-Arnold-Moser) theory, The Arnold conjectures in symplectic topology, The Hilbert-Arnold problem for the number of zeros of abelian integrals, Arnold's inequality, comparison, and complexification method in real algebraic geometry, Arnold-Kolmogorov solution of Hilbert's 13th problem, Arnold's spectral sequence in singularity theory, Arnold diffusion, The Euler-Poincaré-Arnold equations for geodesics on Lie groups, Arnold's stability criterion in hydrodynamics, ABC (Arnold-Beltrami-Childress) ?ows in ?uid dynamics, The Arnold-Korkina dynamo, Arnold's cat map, The Arnold-Liouville theorem in integrable systems, Arnold's continued fractions, Arnold's interpretation of the Maslov index, Arnold's relation in cohomology of braid groups, Arnold tongues in bifurcation theory, The Jordan-Arnold normal forms for families of matrices, The Arnold invariants of plane curves. Arnold wrote some 700 papers, and many books, including 10 university textbooks. He is known for his lucid writing style, which combines mathematical rigour with physical and geometric intuition. Arnold's books on Ordinarydifferentialequations and Mathematical methodsofclassicalmechanics became mathematical bestsellers and integral parts of the mathematical education of students throughout the world.

Algebra --- Partial differential equations --- Mathematical analysis --- Mathematical physics --- differentiaalvergelijkingen --- algebra --- analyse (wiskunde) --- theoretische fysica