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離散数理モデリングセミナー
過去の記録 ～05/02｜次回の予定｜今後の予定 05/03～
| 担当者 | 時弘哲治, ウィロックス ラルフ |
|---|
2024年04月10日(水)
13:30-15:00 数理科学研究科棟(駒場) 056号室
セミナー室変更：470セミナー室→056セミナー室
Jaume Alonso 氏 (Technische Universität Berlin)
Integrable birational maps and a generalisation of QRT to 3D (English)
セミナー室変更：470セミナー室→056セミナー室
Jaume Alonso 氏 (Technische Universität Berlin)
Integrable birational maps and a generalisation of QRT to 3D (English)
[ 講演概要 ]
When completely integrable Hamiltonian systems are discretised, the resulting discrete-time systems are often no longer integrable themselves. This is the so-called problem of integrable discretisation. Two known exceptions to this situation in 3D are the Kahan-Hirota-Kimura discretisations of the Euler top and the Zhukovski-Volterra gyrostat with one non-zero linear parameter β, both birational maps of degree 3. The integrals of these systems define pencils of quadrics. By analysing the geometry of these pencils, we develop a framework that generalises QRT maps and QRT roots to 3D, which allows us to create new integrable maps as a composition of two involutions. We show that under certain geometric conditions, the new maps become of degree 3. We use these results to create new families of discrete integrable maps and we solve the problem of integrability of the Zhukovski-Volterra gyrostat with two β’s.
This is a joint work with Yuri Suris and Kangning Wei.
When completely integrable Hamiltonian systems are discretised, the resulting discrete-time systems are often no longer integrable themselves. This is the so-called problem of integrable discretisation. Two known exceptions to this situation in 3D are the Kahan-Hirota-Kimura discretisations of the Euler top and the Zhukovski-Volterra gyrostat with one non-zero linear parameter β, both birational maps of degree 3. The integrals of these systems define pencils of quadrics. By analysing the geometry of these pencils, we develop a framework that generalises QRT maps and QRT roots to 3D, which allows us to create new integrable maps as a composition of two involutions. We show that under certain geometric conditions, the new maps become of degree 3. We use these results to create new families of discrete integrable maps and we solve the problem of integrability of the Zhukovski-Volterra gyrostat with two β’s.
This is a joint work with Yuri Suris and Kangning Wei.
