On the dynamics of second-order Lagrangian systems
In this article we are concerned with improving the twist condition for second-order Lagrangian systems. We characterize a local Twist property and demonstrate how results on the existence of simple closed characteristics can be extended in the case of the Swift-Hohenberg / extended Fisher-Kolmo...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2017-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2017/101/abstr.html |
| _version_ | 1828834730391371776 |
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| author | Ronald Adams William D. Kalies Robert C. A. M. Vandervorst |
| author_facet | Ronald Adams William D. Kalies Robert C. A. M. Vandervorst |
| author_sort | Ronald Adams |
| collection | DOAJ |
| description | In this article we are concerned with improving the twist condition for
second-order Lagrangian systems. We characterize a local Twist property
and demonstrate how results on the existence of simple closed
characteristics can be extended in the case of the Swift-Hohenberg / extended
Fisher-Kolmogorov Lagrangian. Finally, we describe explicit evolution
equations for broken geodesic curves that could be used to investigate
more general systems or closed characteristics. |
| first_indexed | 2024-12-12T17:45:27Z |
| format | Article |
| id | doaj.art-6c15b399c94c480bad196dcf4c23d6e3 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-12T17:45:27Z |
| publishDate | 2017-04-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-6c15b399c94c480bad196dcf4c23d6e32022-12-22T00:16:57ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912017-04-012017101,118On the dynamics of second-order Lagrangian systemsRonald Adams0William D. Kalies1Robert C. A. M. Vandervorst2 Embry-Riddle Aeronautical Univ., Daytona Beach, FL, USA Florida Atlantic Univ., Boca Raton, FL, USA VU University, Amsterdam, NL In this article we are concerned with improving the twist condition for second-order Lagrangian systems. We characterize a local Twist property and demonstrate how results on the existence of simple closed characteristics can be extended in the case of the Swift-Hohenberg / extended Fisher-Kolmogorov Lagrangian. Finally, we describe explicit evolution equations for broken geodesic curves that could be used to investigate more general systems or closed characteristics.http://ejde.math.txstate.edu/Volumes/2017/101/abstr.htmlSecond-order Lagrangianclosed characteristictwist systemcurve evolution |
| spellingShingle | Ronald Adams William D. Kalies Robert C. A. M. Vandervorst On the dynamics of second-order Lagrangian systems Electronic Journal of Differential Equations Second-order Lagrangian closed characteristic twist system curve evolution |
| title | On the dynamics of second-order Lagrangian systems |
| title_full | On the dynamics of second-order Lagrangian systems |
| title_fullStr | On the dynamics of second-order Lagrangian systems |
| title_full_unstemmed | On the dynamics of second-order Lagrangian systems |
| title_short | On the dynamics of second-order Lagrangian systems |
| title_sort | on the dynamics of second order lagrangian systems |
| topic | Second-order Lagrangian closed characteristic twist system curve evolution |
| url | http://ejde.math.txstate.edu/Volumes/2017/101/abstr.html |
| work_keys_str_mv | AT ronaldadams onthedynamicsofsecondorderlagrangiansystems AT williamdkalies onthedynamicsofsecondorderlagrangiansystems AT robertcamvandervorst onthedynamicsofsecondorderlagrangiansystems |