The Recognition of the Bifurcation Problem with Trivial Solutions
This paper studies the recognition criterion of the bifurcation problem with trivial solution. The <i>t</i>-equivalence is different from the strong equivalence studied by Golubitsky et al. The difference is that the second component of the differential homeomorphism is not identical. Co...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/7/935 |
| _version_ | 1811263364133814272 |
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| author | Yanqing Li Dejian Huang Donghe Pei |
| author_facet | Yanqing Li Dejian Huang Donghe Pei |
| author_sort | Yanqing Li |
| collection | DOAJ |
| description | This paper studies the recognition criterion of the bifurcation problem with trivial solution. The <i>t</i>-equivalence is different from the strong equivalence studied by Golubitsky et al. The difference is that the second component of the differential homeomorphism is not identical. Consider the normal subgroup of <i>t</i>-equivalence group, we obtain the characterization of higher order terms <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="script">P</mi> <mo stretchy="false">(</mo> <mi>h</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>. In addition, we also explore the properties of intrinsic submodules and the finite determinacy of the bifurcation problem. |
| first_indexed | 2024-04-12T19:43:12Z |
| format | Article |
| id | doaj.art-8a6b3c2eda4641939e9c6f079c55ad37 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-12T19:43:12Z |
| publishDate | 2019-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-8a6b3c2eda4641939e9c6f079c55ad372022-12-22T03:19:01ZengMDPI AGSymmetry2073-89942019-07-0111793510.3390/sym11070935sym11070935The Recognition of the Bifurcation Problem with Trivial SolutionsYanqing Li0Dejian Huang1Donghe Pei2School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, ChinaSchool of Mathematics and Statistics, Northeast Normal University, Changchun 130024, ChinaSchool of Mathematics and Statistics, Northeast Normal University, Changchun 130024, ChinaThis paper studies the recognition criterion of the bifurcation problem with trivial solution. The <i>t</i>-equivalence is different from the strong equivalence studied by Golubitsky et al. The difference is that the second component of the differential homeomorphism is not identical. Consider the normal subgroup of <i>t</i>-equivalence group, we obtain the characterization of higher order terms <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="script">P</mi> <mo stretchy="false">(</mo> <mi>h</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>. In addition, we also explore the properties of intrinsic submodules and the finite determinacy of the bifurcation problem.https://www.mdpi.com/2073-8994/11/7/935bifurcationequivalent grouprecognitionintrinsic submodule |
| spellingShingle | Yanqing Li Dejian Huang Donghe Pei The Recognition of the Bifurcation Problem with Trivial Solutions Symmetry bifurcation equivalent group recognition intrinsic submodule |
| title | The Recognition of the Bifurcation Problem with Trivial Solutions |
| title_full | The Recognition of the Bifurcation Problem with Trivial Solutions |
| title_fullStr | The Recognition of the Bifurcation Problem with Trivial Solutions |
| title_full_unstemmed | The Recognition of the Bifurcation Problem with Trivial Solutions |
| title_short | The Recognition of the Bifurcation Problem with Trivial Solutions |
| title_sort | recognition of the bifurcation problem with trivial solutions |
| topic | bifurcation equivalent group recognition intrinsic submodule |
| url | https://www.mdpi.com/2073-8994/11/7/935 |
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