Gradient Trajectories For Plane Singular Metrics I: Oscillating Trajectories
In this short note, we construct an example of a real plane analytic singular metric, degenerating only at the origin, such that any gradient trajectory (respectively to this singular metric) of some well chosen function spirals around the origin. The inversion mapping carries this example into an e...
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| Format: | Article |
| Language: | English |
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De Gruyter
2014-03-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | http://www.degruyter.com/view/j/dema.2014.47.issue-1/dema-2014-0006/dema-2014-0006.xml?format=INT |
| _version_ | 1818228362971185152 |
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| author | Grandjean Vincent |
| author_facet | Grandjean Vincent |
| author_sort | Grandjean Vincent |
| collection | DOAJ |
| description | In this short note, we construct an example of a real plane analytic singular metric, degenerating only at the origin, such that any gradient trajectory (respectively to this singular metric) of some well chosen function spirals around the origin. The inversion mapping carries this example into an example of a gradient spiraling dynamics at infinity |
| first_indexed | 2024-12-12T10:01:31Z |
| format | Article |
| id | doaj.art-880d977ff59c457b8a544d1168194f32 |
| institution | Directory Open Access Journal |
| issn | 0420-1213 2391-4661 |
| language | English |
| last_indexed | 2024-12-12T10:01:31Z |
| publishDate | 2014-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-880d977ff59c457b8a544d1168194f322022-12-22T00:27:58ZengDe GruyterDemonstratio Mathematica0420-12132391-46612014-03-01471697810.2478/dema-2014-0006dema-2014-0006Gradient Trajectories For Plane Singular Metrics I: Oscillating TrajectoriesGrandjean Vincent0DEPARTAMENTO DE MATEMÁTICA, UFC Av. Humberto Monte s/n, Campus do Pici Bloco 914 CEP 60.455-760, FORTALEZA-CE, BRASILIn this short note, we construct an example of a real plane analytic singular metric, degenerating only at the origin, such that any gradient trajectory (respectively to this singular metric) of some well chosen function spirals around the origin. The inversion mapping carries this example into an example of a gradient spiraling dynamics at infinityhttp://www.degruyter.com/view/j/dema.2014.47.issue-1/dema-2014-0006/dema-2014-0006.xml?format=INToscillating and non-oscillating trajectoriessingular gradientsingular metric |
| spellingShingle | Grandjean Vincent Gradient Trajectories For Plane Singular Metrics I: Oscillating Trajectories Demonstratio Mathematica oscillating and non-oscillating trajectories singular gradient singular metric |
| title | Gradient Trajectories For Plane Singular Metrics I: Oscillating Trajectories |
| title_full | Gradient Trajectories For Plane Singular Metrics I: Oscillating Trajectories |
| title_fullStr | Gradient Trajectories For Plane Singular Metrics I: Oscillating Trajectories |
| title_full_unstemmed | Gradient Trajectories For Plane Singular Metrics I: Oscillating Trajectories |
| title_short | Gradient Trajectories For Plane Singular Metrics I: Oscillating Trajectories |
| title_sort | gradient trajectories for plane singular metrics i oscillating trajectories |
| topic | oscillating and non-oscillating trajectories singular gradient singular metric |
| url | http://www.degruyter.com/view/j/dema.2014.47.issue-1/dema-2014-0006/dema-2014-0006.xml?format=INT |
| work_keys_str_mv | AT grandjeanvincent gradienttrajectoriesforplanesingularmetricsioscillatingtrajectories |