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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