000			02153nam a22002177a 4500
003			OSt
005			20230707173147.0
008			220621b |||||||| |||| 00| 0 eng d
020			_a9783642743337
020			_a0387506136
040			_cDonation by Prof. A S Vasudeva Murthy _aICTS-TIFR
050			_aQA614.83
100			_aEkeland Ivar
245			_aConvexity methods in Hamiltonian mechanics
260			_aNew York _bSpringer _c1990
300			_ax, 247 p
520			_aIn the case of completely integrable systems, periodic solutions are found by inspection. For nonintegrable systems, such as the three-body problem in celestial mechanics, they are found by perturbation theory: there is a small parameter € in the problem, the mass of the perturbing body for instance, and for € = 0 the system becomes completely integrable. One then tries to show that its periodic solutions will subsist for € -# 0 small enough. Poincare also introduced global methods, relying on the topological properties of the flow, and the fact that it preserves the 2-form L~=l dPi 1\ dqi' The most celebrated result he obtained in this direction is his last geometric theorem, which states that an area-preserving map of the annulus which rotates the inner circle and the outer circle in opposite directions must have two fixed points. And now another ancient theme appear: the least action principle. It states that the periodic solutions of a Hamiltonian system are extremals of a suitable integral over closed curves. In other words, the problem is variational. This fact was known to Fermat, and Maupertuis put it in the Hamiltonian formalism. In spite of its great aesthetic appeal, the least action principle has had little impact in Hamiltonian mechanics. There is, of course, one exception, Emmy Noether's theorem, which relates integrals ofthe motion to symmetries of the equations. But until recently, no periodic solution had ever been found by variational methods.
856			_uhttps://link.springer.com/book/10.1007/978-3-642-74331-3
856			_uhttps://link.springer.com/book/10.1007/978-3-642-74331-3#toc _yTable of Contents
942			_2lcc _cBK
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