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.
Read Online or Download Hamiltonian and Lagrangian Flows on Center Manifolds: with Applications to Elliptic Variational Problems (Lecture Notes in Mathematics) PDF
Best Mathematical Physics books
Now in its seventh version, Mathematical tools for Physicists keeps to supply all of the mathematical equipment that aspiring scientists and engineers tend to stumble upon as scholars and starting researchers. This bestselling textual content presents mathematical kinfolk and their proofs necessary to the learn of physics and similar fields.
This ebook presents the reader with an simple creation to chaos and fractals, appropriate for college students with a heritage in effortless algebra, with out assuming earlier coursework in calculus or physics. It introduces the foremost phenomena of chaos - aperiodicity, delicate dependence on preliminary stipulations, bifurcations - through easy iterated features.
Hyperbolic Dynamics and Brownian movement illustrates the interaction among precise domain names of arithmetic. there is not any assumption that the reader is a expert in any of those domain names: merely simple wisdom of linear algebra, calculus and chance thought is needed. The content material may be summarized in 3 ways: first of all, this publication presents an creation to hyperbolic geometry, in line with the Lorentz crew.
Additional resources for Hamiltonian and Lagrangian Flows on Center Manifolds: with Applications to Elliptic Variational Problems (Lecture Notes in Mathematics)