|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'506'133
Articles rated: 2609
26 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
On the average principle for one-frequency systems | | Carlo Morosi
; Livio Pizzocchero
; | | Date: |
31 Aug 2005 | | Subject: | Mathematical Physics; Dynamical Systems; Exactly Solvable and Integrable Systems MSC-class: 70K65, 70K70, 34C29, 70H09, 37J40 | math-ph math.DS math.MP nlin.SI | | Affiliation: | Politecnico di Milano), Livio Pizzocchero (Universita’ di Milano | | Abstract: | We consider a perturbed integrable system with one frequency, and the approximate dynamics for the actions given by averaging over the angle. The classical theory grants that, for a perturbation of order epsilon, the error of this approximation is O(epsilon) on a time scale O(1/epsilon), for epsilon -> 0. We replace this qualitative statement with a fully quantitative estimate; in certain cases, our approach also gives a reliable error estimate on time scales larger than 1/epsilon. A number of examples are presented; in many cases our estimator practically coincides with the envelope of the rapidly oscillating distance between the actions of the perturbed and of the averaged systems. Fairly good results are also obtained in some "resonant" cases, where the angular frequency is small along the trajectory of the system. Even though our estimates are proved theoretically, their computation in specific applications typically requires the numerical solution of a system of differential equations. However, the time scale for this system is smaller by a factor epsilon than the time scale for the perturbed system. For this reason, computation of our estimator is faster than the direct numerical solution of the perturbed system; the estimator is rapidly found also in cases when the time scale makes impossible (within reasonable CPU times) or unreliable the direct solution of the perturbed system. | | Source: | arXiv, math-ph/0508067 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER