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Lobe area in adiabatic Hamiltonian systems

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.

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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.

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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.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)ISSA 900024
Department of Energy (DOE)W-7405-ENG-36
Office of Naval Research (ONR)UNSPECIFIED
Issue or Number:1-3
Record Number:CaltechAUTHORS:20170829-080147630
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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, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80886
Deposited By: Tony Diaz
Deposited On:29 Aug 2017 19:32
Last Modified:15 Nov 2021 19:39

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