Mathematical Physics

Download E-books Hamiltonian and Lagrangian Flows on Center Manifolds: with Applications to Elliptic Variational Problems (Lecture Notes in Mathematics) PDF

By Alexander Mielke

The idea of heart manifold relief is studied during this monograph within the context of (infinite-dimensional) Hamil- tonian and Lagrangian platforms. the purpose is to set up a "natural relief process" for Lagrangian structures to their heart manifolds. Nonautonomous difficulties are regarded as good assystems invariant less than the motion of a Lie workforce ( together with the case of relative equilibria). the idea is utilized to elliptic variational problemson cylindrical domain names. hence, all bounded suggestions bifurcating from a trivial country may be defined by means of a discounted finite-dimensional variational challenge of Lagrangian sort. this offers a rigorous justification of rod conception from totally nonlinear third-dimensional elasticity. The e-book might be of curiosity to researchers operating in classical mechanics, dynamical platforms, elliptic variational difficulties, and continuum mechanics. It starts off with the weather of Hamiltonian thought and middle manifold aid in order to make the tools available to non-specialists, from graduate pupil point.

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