Geometri simplektik: Perbedaan antara revisi
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[[Berkas:Limitcycle.svg|jmpl|340px|ka|[[Potret fase]] dari [[oskilator Van der Pol]], sebuah sistem satu dimensional. [[Ruang fase]] adalah obnyek asli dari pembelajaran dalam geometri simplektik.]]
'''Geometri simplektik''' adalah sebuah cabang [[geometri diferensial]] dan [[topologi diferensial]] yang mempelajari manifol-[[manifol simplektik]]; yang merupakan manifol-[[manifol diferensiabel]] yang dialati dengan [[bentuk diferensial|bentuk]] [[bentuk dieferensial tertutup|tertutup]] dan [[bentuk nondegenerasi|nondegenerasi]] Geometri simplektik bermula dari [[mekanika Hamiltonian|perumusan Hamiltonian]] dari [[mekanika klasik]] dimana [[ruang fase]] dari sistem-sistem klasik tertentu ditampatkan pada struktur manifol simplektik.<ref>{{cite news |first=Kevin |last=Hartnett |date=February 9, 2017 |title=A Fight to Fix Geometry’s Foundations |work=[[Quanta Magazine]] |url=https://www.quantamagazine.org/20170209-the-fight-to-fix-symplectic-geometry/ |access-date=2017-09-26 |archive-date=2017-03-15 |archive-url=https://web.archive.org/web/20170315142111/https://www.quantamagazine.org/20170209-the-fight-to-fix-symplectic-geometry/ |dead-url=no }}</ref>
== Pendahuluan ==
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* {{cite book |first=A. T. |last=Fomenko |title=Symplectic Geometry |edition=2nd |year=1995 |publisher=Gordon and Breach |isbn=978-2-88124-901-3 }} ''(An undergraduate level introduction.)''
* {{cite book |first=Maurice A. |last=de Gosson |authorlink=Maurice A. de Gosson |title=Symplectic Geometry and Quantum Mechanics |year=2006 |publisher=Birkhäuser Verlag |location=Basel |isbn=978-3-7643-7574-4 }}
* {{cite journal |first=Alan |last=Weinstein |authorlink=Alan Weinstein |year=1981 |title=Symplectic Geometry |journal=[[Bulletin of the American Mathematical Society]] |volume=5 |issue=1 |pages=1–13 |url=http://www.ams.org/bull/1981-05-01/S0273-0979-1981-14911-9/S0273-0979-1981-14911-9.pdf |doi=10.1090/s0273-0979-1981-14911-9 |access-date=2017-09-26 |archive-date=2023-07-31 |archive-url=https://web.archive.org/web/20230731133850/https://www.ams.org/journals/bull/1981-05-01/S0273-0979-1981-14911-9/S0273-0979-1981-14911-9.pdf |dead-url=no }}
* {{Cite book | last1=Weyl | first1=Hermann | author1-link=Hermann Weyl | title=The Classical Groups. Their Invariants and Representations | year = 1939|ref=harv}} Reprinted by [[Princeton University Press]] (1997). {{ISBN|0-691-05756-7}}. {{MR|0000255}}.
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