Junge, Oliver and Marsden, Jerrold E. and Mezic, Igor (2004) Uncertainty in the dynamics of conservative maps. In: IEEE Conference on Decision and Control, 43rd (CDC 2004), Nassau, Bahamas, 14-17 December 2004. IEEE , Piscataway, NJ, pp. 2225-2230. ISBN 0-7803-8682-5 http://resolver.caltech.edu/CaltechAUTHORS:JUNcdc04
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Abstract
This paper studies the effect of uncertainty, using random perturbations, on area preserving maps of ℝ^2 to itself. We focus on the standard map and a discrete Duffing oscillator as specific examples. We relate the level of uncertainty to the large scale features in the dynamics in a precise way. We also study the effect of such perturbations on bifurcations in such maps. The main tools used for these investigations are a study of the eigenfunction and eigenvalue structure of the associated Perron-Frobenius operator along with set oriented methods for the numerical computations.
| Item Type: | Book Section | ||||||||
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| Additional Information: | © Copyright 2004 IEEE. Reprinted with permission. Publication Date: 17-17 Dec. 2004. Research partially supported by a Max Planck Research Award, NSF-ITR grant ACI-0204932 and AFOSR grant F49620-03-1-0096. | ||||||||
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| Subject Keywords: | bifurcation; eigenvalues and eigenfunctions; large-scale systems; oscillators; perturbation techniques; set theory; uncertain systems; Perron-Frobenius operator; area preserving maps; bifurcations; conservative maps; discrete Duffing oscillator; eigenfunction and eigenvalue structure; large-scale features; numerical computations; random perturbation; set oriented method; uncertainty level | ||||||||
| Record Number: | CaltechAUTHORS:JUNcdc04 | ||||||||
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:JUNcdc04 | ||||||||
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| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||
| ID Code: | 12616 | ||||||||
| Collection: | CaltechAUTHORS | ||||||||
| Deposited By: | Kristin Buxton | ||||||||
| Deposited On: | 15 Dec 2008 22:36 | ||||||||
| Last Modified: | 26 Dec 2012 10:37 |
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