Download Collected Works: Representations of Functions, Celestial by Vladimir I. Arnold (auth.), Alexander B. Givental, Boris A. PDF

By Vladimir I. Arnold (auth.), Alexander B. Givental, Boris A. Khesin, Jerrold E. Marsden, Alexander N. Varchenko, Victor A. Vassiliev, Oleg Ya. Viro, Vladimir M. Zakalyukin (eds.)

Vladimir Arnold is among the nice mathematical scientists of our time. he's well-known for either the breadth and the intensity of his paintings.

At a similar time he's probably the most prolific and notable mathematical authors. this primary quantity of his accrued Works makes a speciality of representations of features, celestial mechanics, and KAM theory.

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Read or Download Collected Works: Representations of Functions, Celestial Mechanics and KAM Theory, 1957–1965 PDF

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Extra info for Collected Works: Representations of Functions, Celestial Mechanics and KAM Theory, 1957–1965

Example text

We now prove that the difference 5 f1 (x, y) = f (x, y) − h(1) q (Φq (x, y)) q=1 satisfies condition (7a), that is, |f1 (x0 , y0 )| 5 M, 6 where (x0 , y0 ) is an arbitrary point of the unit square. I.

Xn−1 ) . 34 On the representation of functions of several variables 11 Fig. 5. In this case we have f (x1 , x2 , . . , xn ) = fxn (x1 , x2 , . . , xn−1 ) n+1 fxrn (x1 , x2 , . . , xn−1 ) = r=1 n+1 fxrn (dr (x1 , x2 , . . , xn−1 )) = r=1 n+1 f r (dr (x1 , x2 , . . , xn−1 ), xn ) , = (1) r=1 where dr (x1 , x2 , . . , xn−1 ) is a map of the domain of definition of the function fxrn (x1 , x2 , . . ) and fxrn (dr ) = f r (dr , xn ) is the map of the point of the ‘standard tree’ dr onto the range of f r (which now depends on xn ).

Jlексных ЧИСJlа а И ~, ЧТО Zi=az1+~ (i= 1, 2 ,••• , n). _Здесь модуль а равен отношению сторон многоугольников А и А о , аргу­ мент - углу поворота, а ~ - комплексное число, изображаемое центром мно­ гоугольника А. z~ +~) n "=1 n 19 n ~Qk (zj) i=l n (1) в вершинах. 246 В. и. АРНОЛЬД = Pk (az + ~)=(a: + ~)k+ а 1 (az + ~)k-l + ..

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