On Some Reversible Cubic Systems
We study three systems from the classification of cubic reversible systems given by Żoła̧dek in 1994. Using affine transformations and elimination algorithms from these three families the six components of the center variety are derived and limit-cycle bifurcations in neighborhoods of the components...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/12/1446 |
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| author | Barbara Arcet Valery G. Romanovski |
| author_facet | Barbara Arcet Valery G. Romanovski |
| author_sort | Barbara Arcet |
| collection | DOAJ |
| description | We study three systems from the classification of cubic reversible systems given by Żoła̧dek in 1994. Using affine transformations and elimination algorithms from these three families the six components of the center variety are derived and limit-cycle bifurcations in neighborhoods of the components are investigated. The invariance of the systems with respect to the generalized involutions introduced by Bastos, Buzzi and Torregrosa in 2021 is discussed. Computations are performed using the computer algebra systems <span style="font-variant: small-caps;">Mathematica</span> and <span style="font-variant: small-caps;">Singular</span>. |
| first_indexed | 2024-03-10T10:13:39Z |
| format | Article |
| id | doaj.art-6182f484b6204772b9c336e1d62a22eb |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T10:13:39Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6182f484b6204772b9c336e1d62a22eb2023-11-22T01:01:30ZengMDPI AGMathematics2227-73902021-06-01912144610.3390/math9121446On Some Reversible Cubic SystemsBarbara Arcet0Valery G. Romanovski1Center for Applied Mathematics and Theoretical Physics, University of Maribor, 2000 Maribor, SloveniaCenter for Applied Mathematics and Theoretical Physics, University of Maribor, 2000 Maribor, SloveniaWe study three systems from the classification of cubic reversible systems given by Żoła̧dek in 1994. Using affine transformations and elimination algorithms from these three families the six components of the center variety are derived and limit-cycle bifurcations in neighborhoods of the components are investigated. The invariance of the systems with respect to the generalized involutions introduced by Bastos, Buzzi and Torregrosa in 2021 is discussed. Computations are performed using the computer algebra systems <span style="font-variant: small-caps;">Mathematica</span> and <span style="font-variant: small-caps;">Singular</span>.https://www.mdpi.com/2227-7390/9/12/1446centersreversibilitycubic systemsinvolutionlimit cycles |
| spellingShingle | Barbara Arcet Valery G. Romanovski On Some Reversible Cubic Systems Mathematics centers reversibility cubic systems involution limit cycles |
| title | On Some Reversible Cubic Systems |
| title_full | On Some Reversible Cubic Systems |
| title_fullStr | On Some Reversible Cubic Systems |
| title_full_unstemmed | On Some Reversible Cubic Systems |
| title_short | On Some Reversible Cubic Systems |
| title_sort | on some reversible cubic systems |
| topic | centers reversibility cubic systems involution limit cycles |
| url | https://www.mdpi.com/2227-7390/9/12/1446 |
| work_keys_str_mv | AT barbaraarcet onsomereversiblecubicsystems AT valerygromanovski onsomereversiblecubicsystems |