Titlebook: Vladimir I. Arnold - Collected Works; Hydrodynamics, Bifur Vladimir I. Arnold,Alexander B. Givental,Boris A. Book 2014 Springer-Verlag Ber

Inclement

On the differential geometry of infinite-dimensional Lie groups and its application to the hydrodyny of Euler’s equations by a modern exposition of the question..The eulerian motions of a rigid body are the geodesics on the group of rotations of three dimensional euclidean space endowed with a left invariant metric. Basically, Euler’s theory makes use of nothing but this circumstance; hence Euler

ASSAY

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On a characteristic class arising in quantization conditions, any number of conjugate points [1, 2]. It turned out that there appeared in the asymptotic formulas certain integers, reflecting homological properties of curves on surfaces of the phase space and closely related to the Morse indexes of the corresponding variational problems. In particular, Maslov

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gait-cycle

使混合

Remarks on singularities of finite codimension in complex dynamical systems,ng multiple roots is the space .(π ,1) for the group .(.) of braids on n strands:.π.(..) = .(.), π.(..) = 0for. > 1. (1).This connection can be used in both directions: both for the study of braid groups and for the study of algebraic functions. Here are some examples.

过剩

Hamiltonian nature of the Euler equations in the dynamics of a rigid body and of an ideal fluid,n general position″ were investigated by Poincaré [3] and Zigel’ [4]. They showed that in a neighborhood of a singular (that is, fixed) point in general position an analytic dynamical system is linear in a suitable analytic system of coordinates.

induct

On cohomology classes of algebraic functions invariant under Tschirnhausen transformations,ordinary differential equations one deals with the decomposition of the space of vector fields with zero at . into two classes: the class of fields for which the point . is stable, and the class of fields for which the point . is unstable.

Jingoism

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d many books.19 notions named after Arnold.Second volume of 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 o