Differential Equations

Read e-book online Introduction to the Perturbation Theory of Hamiltonian PDF

By Dmitry Treschev,Oleg Zubelevich

This booklet is a longer model of lectures given by means of the ?rst writer in 1995–1996 on the division of Mechanics and arithmetic of Moscow nation college. We think significant a part of the e-book should be considered as an extra fabric to the traditional process Hamiltonian mechanics. compared to the unique Russian 1 model we have now integrated new fabric, simpli?ed a few proofs and corrected m- prints. Hamiltonian equations ?rst seemed in reference to difficulties of geometric optics and celestial mechanics. Later it grew to become transparent that those equations describe a wide classof systemsin classical mechanics,physics,chemistry,and otherdomains. Hamiltonian structures and their discrete analogs play a simple position in such difficulties as inflexible physique dynamics, geodesics on Riemann surfaces, quasi-classic approximation in quantum mechanics, cosmological types, dynamics of debris in an accel- ator, billiards and different platforms with elastic re?ections, many in?nite-dimensional versions in mathematical physics, and so forth. during this publication we learn Hamiltonian platforms assuming that they rely on a few parameter (usually?), the place for?= zero the dynamics is in a feeling easy (as a rule, integrable). often the sort of parameter appears to be like obviously. for instance, in celestial mechanics it truly is accredited to take? equivalent to the ratio: the mass of Jupiter over the mass of the sunlight. In different circumstances it's attainable to introduce the small parameter ar- ?cially.

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Introduction to the Perturbation Theory of Hamiltonian Systems (Springer Monographs in Mathematics) by Dmitry Treschev,Oleg Zubelevich

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