Solutions of the Loewner equation with combined driving functions
The paper is devoted to the multiple chordal Loewner differential equation with different driving functions on two time intervals. We obtain exact implicit or explicit solutions to the Loewner equations with piecewise constant driving functions and with combined constant and square root driving func...
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| Format: | Article |
| Language: | English |
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Saratov State University
2021-08-01
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| Series: | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
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| Online Access: | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2021/08/317-325_prokhorov_et_al.pdf |
| _version_ | 1818356154223296512 |
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| author | Prokhorov, Dmitri Valentinovich Zakharov, Andrei Mikhailovich Zherdev, Andrey V. |
| author_facet | Prokhorov, Dmitri Valentinovich Zakharov, Andrei Mikhailovich Zherdev, Andrey V. |
| author_sort | Prokhorov, Dmitri Valentinovich |
| collection | DOAJ |
| description | The paper is devoted to the multiple chordal Loewner differential equation with different driving functions on two time intervals. We obtain exact implicit or explicit solutions to the Loewner equations with piecewise constant driving functions and with combined constant and square root driving functions. In both cases, there is an analytical and geometrical description of generated traces. Earlier, Kager, Nienhuis and Kadanoff integrated the chordal Loewner differential equation either with a constant driving function or with a square root driving function. In the first case, the equation generates a rectilinear slit in the upper half-plane which is orthogonal to the real axis $\mathbb R$. In the second case, a rectilinear slit forms an angle to $\mathbb R$. In our paper, the multiple chordal Loewner differential equation generates more complicated hulls consisting of three rectilinear and curvilinear fragments which can be either intersecting or disjoint. Analytical results of the paper are accompanied by geometrical illustrations. |
| first_indexed | 2024-12-13T19:52:42Z |
| format | Article |
| id | doaj.art-871577b007e148ffb6b21ec0daa4415d |
| institution | Directory Open Access Journal |
| issn | 1816-9791 2541-9005 |
| language | English |
| last_indexed | 2024-12-13T19:52:42Z |
| publishDate | 2021-08-01 |
| publisher | Saratov State University |
| record_format | Article |
| series | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
| spelling | doaj.art-871577b007e148ffb6b21ec0daa4415d2022-12-21T23:33:23ZengSaratov State UniversityИзвестия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика1816-97912541-90052021-08-0121331732510.18500/1816-9791-2021-21-3-317-325Solutions of the Loewner equation with combined driving functionsProkhorov, Dmitri Valentinovich0Zakharov, Andrei Mikhailovich1Zherdev, Andrey V.2Saratov State University, Russia, 410026, Saratov, Astrahanskaya str., 83Saratov State University, Russia, 410026, Saratov, Astrahanskaya str., 83Saratov State University, Russia, 410026, Saratov, Astrahanskaya str., 83The paper is devoted to the multiple chordal Loewner differential equation with different driving functions on two time intervals. We obtain exact implicit or explicit solutions to the Loewner equations with piecewise constant driving functions and with combined constant and square root driving functions. In both cases, there is an analytical and geometrical description of generated traces. Earlier, Kager, Nienhuis and Kadanoff integrated the chordal Loewner differential equation either with a constant driving function or with a square root driving function. In the first case, the equation generates a rectilinear slit in the upper half-plane which is orthogonal to the real axis $\mathbb R$. In the second case, a rectilinear slit forms an angle to $\mathbb R$. In our paper, the multiple chordal Loewner differential equation generates more complicated hulls consisting of three rectilinear and curvilinear fragments which can be either intersecting or disjoint. Analytical results of the paper are accompanied by geometrical illustrations.https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2021/08/317-325_prokhorov_et_al.pdfloewner equationdriving functiontraceintegrability case |
| spellingShingle | Prokhorov, Dmitri Valentinovich Zakharov, Andrei Mikhailovich Zherdev, Andrey V. Solutions of the Loewner equation with combined driving functions Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика loewner equation driving function trace integrability case |
| title | Solutions of the Loewner equation with combined driving functions |
| title_full | Solutions of the Loewner equation with combined driving functions |
| title_fullStr | Solutions of the Loewner equation with combined driving functions |
| title_full_unstemmed | Solutions of the Loewner equation with combined driving functions |
| title_short | Solutions of the Loewner equation with combined driving functions |
| title_sort | solutions of the loewner equation with combined driving functions |
| topic | loewner equation driving function trace integrability case |
| url | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2021/08/317-325_prokhorov_et_al.pdf |
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