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 stated by means of Vladimir Arnold in his recognized seminar at Moscow country collage over a number of many years. furthermore, there are difficulties released in his a number of papers and books.

The invariable peculiarity of those difficulties used to be that Arnold didn't think of arithmetic a online game with deductive reasoning and logos, yet part of ordinary technological know-how (especially of physics), i.e. an experimental technological know-how. lots of those difficulties are nonetheless on the frontier of analysis this day and are nonetheless open, or even those who are more often than not solved continue stimulating new learn, showing each year in journals worldwide.

The moment a part of the publication is a set of commentaries, in general through Arnold's former scholars, at the present development within the difficulties' options (featuring a bibliography encouraged by way of them).

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

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**Extra info for Arnold's Problems**

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In this case its interlacing by the spectrum of a close system with (X — 1 degrees of freedom would follow from the Rayleigh-Courant-Fisher theory. 38 The Problems 1979-4 1979-4. Construct a "complexification" of the homology theory (replacing a boundary with a two-sheet branched covering). What is the complexification of orientation? ) 1979-5. Construct the characteristic classes of Lagrangian singularities from the stable cohomology ring of complements of caustics. 1979-6. Do the real and the complex modality for a critical point of a function always coincide?

Evaluate the cohomology rings L/t = lim nn+icT'kn, where Xn are the taun—>°° tological Grassmann bundles over U(n)/O(«) or over U(n)/SO(n), and T is the Thorn space. 1981-7. A quasifunction is an exact Lagrangian embedded submanifold of T*V that is isotopic to the zero section in the class of such embeddings. Critical points are intersections with the zero section. Conjecture: the number of critical points for a quasifunction is not less than for a function. 1981-8. What function on the collar can be extended over the ball without critical points?

In the theory of singularities (e. , critical points of functions), why is the codimension in the real case the same as in the complex case? Compare with the R- and C-modality and with the {co)dimension of the prolonged self-intersection line of the swallowtail or the umbrella. 1980-9. Apply mixed Hodge structures to real algebraic geometry. For example, for estimation of topological invariants of real Morsifications, and for investigation of the topology of discriminants. 42 The Problems 1980-10 1980-10.

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

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