On Two Remarkable Groups of Area-Preserving Homeomorphisms
We prove that on a symplectic sphere, the group of Hamiltonian homeomorphisms in the sense of Oh and Müller is a proper normal subgroup of the group of finite energy Hamiltonian homeomorphisms. Moreover we detect infinite-dimensional flats inside the quotient of these groups endowed with the natural...
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| Date: | 2023 |
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| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2023
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| Online Access: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1011 |
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| Journal Title: | Journal of Mathematical Physics, Analysis, Geometry |
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oai:jmag.ilt.kharkiv.ua:article-10112024-10-11T14:48:59Z On Two Remarkable Groups of Area-Preserving Homeomorphisms On Two Remarkable Groups of Area-Preserving Homeomorphisms On Two Remarkable Groups of Area-Preserving Homeomorphisms Buhovsky, Lev гамiльтоновi гомеоморфiзми гiпотеза Фатi метрика Гофера спектральнi iнварiанти Hamiltonian homeomorphisms Fathi conjecture Hofer metric spectral invariants We prove that on a symplectic sphere, the group of Hamiltonian homeomorphisms in the sense of Oh and Müller is a proper normal subgroup of the group of finite energy Hamiltonian homeomorphisms. Moreover we detect infinite-dimensional flats inside the quotient of these groups endowed with the natural Hofer pseudo-metric. Mathematical Subject Classification 2020: 53D05 Ми доводимо, що на симплектичнiй сферi група гамiльтонових гомеоморфiзмiв в сенсi Ога i Мюллера є власною нормальною пiдгрупою гамiльтонових гомеоморфiзмiв зi скiнченною енергiєю. Бiльш того, ми знаходимо скiнченновимiрнi пласкi модулi, надiленi природною псевдометрикою Гофера, у факторгрупi цих груп. Mathematical Subject Classification 2020: 53D05 Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України 2023-07-31 Article Article application/pdf https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1011 10.15407/mag19.02.339 Journal of Mathematical Physics, Analysis, Geometry; Vol. 19 No. 2 (2023): Dedicated to Volodymyr Marchenko's 100th birthday; 339–373 Журнал математической физики, анализа, геометрии; Том 19 № 2 (2023): Присвячений 100-річчю від дня народження Володимира Олександровича Марченка; 339–373 Журнал математичної фізики, аналізу, геометрії; Том 19 № 2 (2023): Присвячений 100-річчю від дня народження Володимира Олександровича Марченка; 339–373 1817-5805 1812-9471 en https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1011/jm19-0339e |
| institution |
Journal of Mathematical Physics, Analysis, Geometry |
| baseUrl_str |
|
| datestamp_date |
2024-10-11T14:48:59Z |
| collection |
OJS |
| language |
English |
| topic |
гамiльтоновi гомеоморфiзми гiпотеза Фатi метрика Гофера спектральнi iнварiанти |
| spellingShingle |
гамiльтоновi гомеоморфiзми гiпотеза Фатi метрика Гофера спектральнi iнварiанти Buhovsky, Lev On Two Remarkable Groups of Area-Preserving Homeomorphisms |
| topic_facet |
гамiльтоновi гомеоморфiзми гiпотеза Фатi метрика Гофера спектральнi iнварiанти Hamiltonian homeomorphisms Fathi conjecture Hofer metric spectral invariants |
| format |
Article |
| author |
Buhovsky, Lev |
| author_facet |
Buhovsky, Lev |
| author_sort |
Buhovsky, Lev |
| title |
On Two Remarkable Groups of Area-Preserving Homeomorphisms |
| title_short |
On Two Remarkable Groups of Area-Preserving Homeomorphisms |
| title_full |
On Two Remarkable Groups of Area-Preserving Homeomorphisms |
| title_fullStr |
On Two Remarkable Groups of Area-Preserving Homeomorphisms |
| title_full_unstemmed |
On Two Remarkable Groups of Area-Preserving Homeomorphisms |
| title_sort |
on two remarkable groups of area-preserving homeomorphisms |
| title_alt |
On Two Remarkable Groups of Area-Preserving Homeomorphisms On Two Remarkable Groups of Area-Preserving Homeomorphisms |
| description |
We prove that on a symplectic sphere, the group of Hamiltonian homeomorphisms in the sense of Oh and Müller is a proper normal subgroup of the group of finite energy Hamiltonian homeomorphisms. Moreover we detect infinite-dimensional flats inside the quotient of these groups endowed with the natural Hofer pseudo-metric.
Mathematical Subject Classification 2020: 53D05 |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України |
| publishDate |
2023 |
| url |
https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1011 |
| work_keys_str_mv |
AT buhovskylev ontworemarkablegroupsofareapreservinghomeomorphisms |
| first_indexed |
2025-09-26T01:40:36Z |
| last_indexed |
2025-09-26T01:40:36Z |
| _version_ |
1850836702908645376 |