Kaper, Tasso J. and Wiggins, Stephen (1991) Lobe area in adiabatic Hamiltonian systems. Physica D, 51 (1-3). pp. 205-212. ISSN 0167-2789. doi:10.1016/0167-2789(91)90233-Y. https://resolver.caltech.edu/CaltechAUTHORS:20170829-080147630
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Abstract
We establish an analytically computable formula based on the adiabatic Melnikov function for lobe area in one-degree-of-freedom Hamiltonian systems depending on a parameter which varies slowly in time. We illustrate this lobe area result on a slowly, parametrically forced pendulum, a paradigm problem for adiabatic chaos. Our analysis unites the theory of action from classical mechanics with the theory of the adiabatic Melnikov function from the field of global bifurcation theory.
| Item Type: | Article | ||||||||||
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| Additional Information: | © 1991 Elsevier B.V. This research was partially supported by AFOSR ISSA 900024, DOE Contract W-7405-ENG-36, an NSF Presidential Young Investigator Award, and an ONR Young Investigator Award. Part of this work was done when the authors worked at the CNLS in Los Alamos. | ||||||||||
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| Issue or Number: | 1-3 | ||||||||||
| DOI: | 10.1016/0167-2789(91)90233-Y | ||||||||||
| Record Number: | CaltechAUTHORS:20170829-080147630 | ||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170829-080147630 | ||||||||||
| Official Citation: | Tasso J. Kaper, Stephen Wiggins, Lobe area in adiabatic Hamiltonian systems, Physica D: Nonlinear Phenomena, Volume 51, Issues 1–3, August 1991, Pages 205-212, ISSN 0167-2789, https://doi.org/10.1016/0167-2789(91)90233-Y. (http://www.sciencedirect.com/science/article/pii/016727899190233Y) | ||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||
| ID Code: | 80886 | ||||||||||
| Collection: | CaltechAUTHORS | ||||||||||
| Deposited By: | Tony Diaz | ||||||||||
| Deposited On: | 29 Aug 2017 19:32 | ||||||||||
| Last Modified: | 15 Nov 2021 19:39 |
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