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SUMMARY:A 3D generalisation of QRT and the construction of integrable bira
 tional systems
DTSTART;VALUE=DATE-TIME:20230622T133000Z
DTEND;VALUE=DATE-TIME:20230622T140000Z
DTSTAMP;VALUE=DATE-TIME:20260725T234554Z
UID:indico-contribution-13@cern.ch
DESCRIPTION:Speakers: Dr. ALONSO\, Jaume (Technische Universitaet Berlin)\
 nWhen completely integrable Hamiltonian systems are discretised\, the resu
 lting discrete-time systems are often no longer integrable themselves. Thi
 s is the so-called "problem of integrable discretisation". Two known excep
 tions to this situation in 3D are the Kahan discretisations of the Euler t
 op and the Zhukovski-Volterra gyrostat with one non-zero linear parameter 
 $\\beta$\, both of degree 3. The integrals of these systems define pencils
  of quadrics. By analysing the geometry of these pencils\, we develop a fr
 amework that \ngeneralises 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 gyrost
 at with two $\\beta$'s.\n\nThis is a joint work with Yuri Suris and Kangni
 ng Wei.\n\nhttp://indico.fuw.edu.pl/contributionDisplay.py?contribId=13&se
 ssionId=9&confId=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=13&sessionId
 =9&confId=67
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