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SUMMARY:Alex Haro (University of Barcelona)
DTSTART:20201202T200000Z
DTEND:20201202T210000Z
DTSTAMP:20260423T021423Z
UID:ONEPAS/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ONEPAS/10/">
 Computer-assisted applications of KAM theory</a>\nby Alex Haro (University
  of Barcelona) as part of Online Northeast PDE and Analysis Seminar\n\n\nA
 bstract\nStability of Hamiltonian systems is relevant to problems from cel
 estial mechanics\, particle accelerators\, plasma confinement\, quasigeost
 rophic flows\, etc. Motivated by such applications\, one is interested in 
 detecting mechanisms of stability in concrete models\, and in providing qu
 antitative information on the stable trajectories. KAM theory concerns the
  existence of quasi-periodic solutions\, that are geometrically described 
 as orbits lying inside invariant tori.\n                                  
                                           <br> <br>\n                     
                                                        In this lecture we 
 will overview a methodology for rigorously detecting  quasi-periodic orbit
 s in Hamiltonian systems. The methodology involves analytical\, geometrica
 l and computational methods and covers from pen and paper rigorous results
  to computer-assisted rigorous results\, passing through algorithms (and t
 he study of their convergence) and implementations.   We will present some
  ideas for performing computer assisted proofs in this context. In particu
 lar\, we will see FFT-methods for representing rigorously real-analytic pe
 riodic functions\, that are used to parameterize tori in phase space. We w
 ill see some applications in this context.  We will finish the lecture wit
 h some other applications and further topics.\n
LOCATION:https://researchseminars.org/talk/ONEPAS/10/
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