By Vladimir I. Arnold

ISBN-10: 3540206140

ISBN-13: 9783540206149

ISBN-10: 3540207481

ISBN-13: 9783540207481

ISBN-10: 3540268669

ISBN-13: 9783540268666

Arnold's difficulties comprises mathematical difficulties cited via Vladimir Arnold in his recognized seminar at Moscow kingdom college over a number of a long time. furthermore, there are difficulties released in his a number of papers and books.

The invariable peculiarity of those difficulties was once that Arnold didn't think about arithmetic a online game with deductive reasoning and emblems, yet part of ordinary technological know-how (especially of physics), i.e. an experimental technology. lots of those difficulties are nonetheless on the frontier of analysis this present day and are nonetheless open, or even those who are normally solved retain stimulating new study, showing each year in journals world wide.

The moment a part of the publication is a set of commentaries, normally by means of Arnold's former scholars, at the present development within the difficulties' ideas (featuring a bibliography encouraged via them).

This e-book can be of significant curiosity to researchers and graduate scholars in arithmetic and mathematical physics.

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**Extra resources for Arnold's Problems**

**Sample text**

1976-38. Determine the singularities and other analytic properties of thermodynamic functions when the interaction potential is known. 32 The Problems 1976-39 1976-39. Does a symplectic diffeomorphism of the two-dimensional torus have a fixed point whenever this diffeomorphism is homologous to the identity? 1976-40. What could be the mathematical equivalent of the physical notion of turbulence? One of the aspects of this question: find "good" theorems of existence and uniqueness for the 3-dimensional Navier-Stokes equations.

Classify the simple singularities of functions on a manifold with an action of a group (for example, finite) up to equivariant diffeomorphisms (commuting with the group action). 1974-8. Investigate the typical perestroikas of a wave front moving with time (and of the corresponding Legendrian map). 1974-9. Give a topological classification of the Legendrian singularities corresponding to the parabolic critical points of functions. 1974-10. A conic singularity over a given base carries topological invariants of the base into the singular point.

Investigate the singularities of implicit differential equations (both ordinary and partial). 1976-1. Given a system of Newton polyhedra, is there a system of real polynomials with these polyhedra which has the correct number of real roots (i. , the same as for a system with generic complex coefficients)? 1976-2. Consider two plane polynomial vector fields of degrees m and n, respectively. Is it possible to estimate the number of intersection points of their limit cycles in terms of n and m (find a sharp attainable estimate)?

### Arnold's Problems by Vladimir I. Arnold

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