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This volume contains articles written by V. I. Arnold's colleagues on the occasion of his 60th birthday. The articles are mostly devoted to various aspects of geometry of differential equations and relations to global analysis and Hamiltonian mechanics.
Lagrangian reduction, the Euler-Poincare equations, and semidirect products by H. Cendra, D. D. Holm, J. E. Marsden, and T. S. Ratiu Lagrangian intersection theory: Finite-dimensional approach by Y. Eliashberg and M. Gromov Multiplicity of a Noetherian intersection by A. Gabrielov and A. Khovanskii Sixth Painleve equation, universal elliptic curve, and mirror of ${\mathbf P}^2$ by Yu. I. Manin Convex hulls of random processes by Ya. G. Sinai Mutual position of hypersurfaces in projective space by O. Viro Hochschild cohomology and characteristic classes for star-products by A. Weinstein and P. Xu.