Weak convergence and averaging for ODE
| Autor: | Lawrence C. Evans, Te Zhang |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Hamiltonian mechanics
Weak convergence Applied Mathematics Mathematical analysis Ergodicity Degrees of freedom (physics and chemistry) Ode 01 natural sciences 010305 fluids & plasmas Inverted pendulum symbols.namesake Simple (abstract algebra) Electric field 0103 physical sciences symbols 010306 general physics Analysis Mathematics |
| Zdroj: | Nonlinear Analysis. 138:83-92 |
| ISSN: | 0362-546X |
| DOI: | 10.1016/j.na.2015.10.011 |
| Popis: | This mostly expository paper shows how weak convergence methods provide simple, elegant proofs of (i) the stabilization of an inverted pendulum under fast vertical oscillations, (ii) the existence of particle traps induced by rapidly varying electric fields and (iii) the adiabatic invariance of ∫ Γ p d x for slowing varying planar Hamiltonian dynamics. Under an appropriate, but very restrictive, unique ergodicity assumption, the proof of (iii) extends also to many degrees of freedom. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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