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SUMMARY:Degree growth calculations for lattice equations
DTSTART;VALUE=DATE-TIME:20230622T093000Z
DTEND;VALUE=DATE-TIME:20230622T100000Z
DTSTAMP;VALUE=DATE-TIME:20260423T220359Z
UID:indico-contribution-21@cern.ch
DESCRIPTION:Speakers: Dr. MASE\, Takafumi (the University of Tokyo)\nInteg
 rability criteria that have been enormously successful for second order ma
 ppings\, such as singularity confinement or zero algebraic entropy\, are o
 ften applied to lattice equations as though the latter were mere mappings.
 \nIn this talk we will show that such a naïve approach can (and does) lea
 d to all sorts of contradictions and that considerable care is needed when
  using such methods to investigate the integrability of a given lattice eq
 uation.\n\nMore precisely:\nIn this talk we show that the results of degre
 e growth calculations for lattice equations strongly depend on the initial
  value problem that one chooses\, either because of problems that arise in
  the past light-cone\, or because of interferences in the future light-con
 e.\nAmong the examples we treat are initial value problems for dKdV\, disc
 rete Liouville and dToda\, for which the degree growth becomes exponential
 \, in contrast to the common belief that discrete integrable equations mus
 t have polynomial growth and that linearizable equations necessarily have 
 linear degree growth\, regardless of the initial value problem one imposes
 .\nFinally\, as a possible remedy for one of the observed anomalies\, we a
 lso propose basing integrability tests that use growth criteria on the deg
 ree growth of a single initial value instead of all the initial values.\n\
 nReference:\nJ. Hietarinta\, T. Mase & R. Willox: J. Phys. A: Math. Theor.
  52 49LT01 (2019).\n\nhttp://indico.fuw.edu.pl/contributionDisplay.py?cont
 ribId=21&sessionId=2&confId=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=21&sessionId
 =2&confId=67
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