Wiggins, Stephen and Holmes, Philip (1987) Homoclinic Orbits In Slowly Varying Oscillators. SIAM Journal on Mathematical Analysis, 18 (3). pp. 612-629. ISSN 0036-1410. doi:10.1137/0518047. https://resolver.caltech.edu/CaltechAUTHORS:20120621-165755675
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Abstract
We obtain existence and bifurcation theorems for homoclinic orbits in three-dimensional flows that are perturbations of families of planar Hamiltonian systems. The perturbations may or may not depend explicitly on time. We show how the results on periodic orbits of the preceding paper are related to the present homoclinic results, and apply them to a periodically forced Duffing equation with weak feedback.
| Item Type: | Article | |||||||||
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| Additional Information: | © 1987 Society for Industrial and Applied Mathematics. Received June 1, 1985; accepted for publication (in revised form) April 22, 1986; Published online February 17, 2012. This research was supported in part by the Air Force Office of Scientific Research under AFSOR 84-0051. | |||||||||
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| Subject Keywords: | bifurcation; Hamiltonian system; homoclinic orbit; perturbation theory; Melnikov method | |||||||||
| Issue or Number: | 3 | |||||||||
| Classification Code: | AMS Subject Headings: 34CXX; 58F14; 70KXX | |||||||||
| DOI: | 10.1137/0518047 | |||||||||
| Record Number: | CaltechAUTHORS:20120621-165755675 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20120621-165755675 | |||||||||
| Official Citation: | Homoclinic Orbits in Slowly Varying Oscillators Wiggins, S. and Holmes, P. SIAM Journal on Mathematical Analysis 1987 18:3, 612-629 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 32020 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | INVALID USER | |||||||||
| Deposited On: | 22 Jun 2012 20:17 | |||||||||
| Last Modified: | 09 Nov 2021 20:03 |
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