On the maximum number of period annuli for second order conservative equations
We consider a second order scalar conservative differential equation whose potential function is a Morse function with a finite number of critical points and is unbounded at infinity. We give an upper bound for the number of nonglobal nontrivial period annuli of the equation and prove that the upper...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2021-11-01
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| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/13979 |
| _version_ | 1831518923869126656 |
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| author | Armands Gritsans Inara Yermachenko |
| author_facet | Armands Gritsans Inara Yermachenko |
| author_sort | Armands Gritsans |
| collection | DOAJ |
| description | We consider a second order scalar conservative differential equation whose potential function is a Morse function with a finite number of critical points and is unbounded at infinity. We give an upper bound for the number of nonglobal nontrivial period annuli of the equation and prove that the upper bound obtained is sharp. We use tree theory in our considerations. |
| first_indexed | 2024-12-13T16:04:02Z |
| format | Article |
| id | doaj.art-fc54a7ad90ec49ea83dc9abd3dc3d582 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-13T16:04:02Z |
| publishDate | 2021-11-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-fc54a7ad90ec49ea83dc9abd3dc3d5822022-12-21T23:39:06ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102021-11-0126461263010.3846/mma.2021.1397913979On the maximum number of period annuli for second order conservative equationsArmands Gritsans0Inara Yermachenko1Daugavpils University, Institute of Life Sciences and Technology, Parādes str. 1, LV-5400 Daugavpils, LatviaDaugavpils University, Institute of Life Sciences and Technology, Parādes str. 1, LV-5400 Daugavpils, LatviaWe consider a second order scalar conservative differential equation whose potential function is a Morse function with a finite number of critical points and is unbounded at infinity. We give an upper bound for the number of nonglobal nontrivial period annuli of the equation and prove that the upper bound obtained is sharp. We use tree theory in our considerations.https://journals.vgtu.lt/index.php/MMA/article/view/13979conservative equationmorse functionperiod annulusbinary tree |
| spellingShingle | Armands Gritsans Inara Yermachenko On the maximum number of period annuli for second order conservative equations Mathematical Modelling and Analysis conservative equation morse function period annulus binary tree |
| title | On the maximum number of period annuli for second order conservative equations |
| title_full | On the maximum number of period annuli for second order conservative equations |
| title_fullStr | On the maximum number of period annuli for second order conservative equations |
| title_full_unstemmed | On the maximum number of period annuli for second order conservative equations |
| title_short | On the maximum number of period annuli for second order conservative equations |
| title_sort | on the maximum number of period annuli for second order conservative equations |
| topic | conservative equation morse function period annulus binary tree |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/13979 |
| work_keys_str_mv | AT armandsgritsans onthemaximumnumberofperiodannuliforsecondorderconservativeequations AT inarayermachenko onthemaximumnumberofperiodannuliforsecondorderconservativeequations |