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SUMMARY:Tere M. Seara --- An introduction to geometric methods in Arnold d
 iffusion
DTSTART:20260327T130000Z
DTEND:20260327T140000Z
DTSTAMP:20260607T054200Z
UID:indico-event-16245@indico.math.cnrs.fr
DESCRIPTION: In this seminar\, I will provide an overview of the so-calle
 d geometric methods in Arnold diffusion. Arnold diffusion occurs in pertur
 bations of integrable systems. In such systems\, when written in action-an
 gle variables\, the action does not evolve under the flow (it is a first i
 ntegral of motion). Roughly speaking\, a system undergoes Arnold diffusion
  when\, for arbitrarily small "typical" perturbations\, the change in acti
 ons becomes of order one (independent of the parameter values). Several m
 ethods have been used to detect this phenomenon. In this talk\, we will re
 view the geometric methods\, introducing concepts such as Normally Hyperbo
 lic Invariant Manifolds (NHIM) and their stable and unstable manifolds. W
 hen these manifolds intersect along a "homoclinic channel"\, one can defin
 e the "Scattering map"\, which encodes the heteroclinic connections betwee
 n points on the NHIM.  By combining iterations of the Scattering map with
  the internal dynamics of the NHIM\, we will find "pseudo-orbits" along wh
 ich the action increases. These orbits will be followed by real orbits whe
 re the action also increases. Finally\, we will apply this methodology to
  the famous example provided by Arnold in 1964.\n\nhttps://indico.math.cnr
 s.fr/event/16245/
LOCATION:Amphithéâtre Charles Hermite (IHP - Bâtiment Borel)
URL:https://indico.math.cnrs.fr/event/16245/
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