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SUMMARY:Cotangent Bundle Reduction and its Applications to Poincaré-Birkh
 off Normal Forms: Analysis of Reactions in Rotating Molecules
DTSTART:20141001T163000
DTEND:20141001T173000
DTSTAMP:20260407T043640Z
UID:8961fe79d6f1058a2d7befa01e3f934ca03314717334f892c70ab33d
CATEGORIES:Conferences - Seminars
DESCRIPTION:Ünver Çiftçi (EPFL)\nGeometry and Dynamics SeminarAbstract:
  Reaction type dynamics arises due to the presence of bottlenecks in the s
 ystem's phase space. Such bottlenecks are typically induced by saddle type
  equilibrium points. In recent years it has been shown that the transport 
 through such bottlenecks is governed by various phase space structures. Th
 ese phase space structures can be constructed from a Poincaré-Birkhoff no
 rmal form. To study reactions in rotating molecules modeled by N-body syst
 ems one has to reduce the rotational symmetry and study the phase space bo
 ttlenecks induced by the saddle type relative equilibria of the reduced sy
 stem.\nIn the first part of the talk\, I will outline a systematic and nat
 ural construction of canonical coordinates for the reduced space of a cota
 ngent bundle with a free Lie group action. The canonical coordinates enabl
 e us to compute Poincaré-Birkhoff normal forms of relative equilibria usi
 ng standard algorithms. The case of natural mechanical systems with symmet
 ries will be considered in some detail. As examples I will give computatio
 ns of Poincaré-Birkhoff normal forms for a Lagrangian equilateral triangl
 e configuration of a three-body system with a Morse-type potential and the
  stretched-out configuration of a double spherical pendulum. In the second
  part\, I will talk about how the construction of phase space structures c
 an be generalized to the case of the relative equilibria of a rotational s
 ymmetry reduced three-body system. My main example will be the isomerizati
 on reaction of the HCN molecule. Time permitting I want to introduce a new
  type of bottleneck which mediates kinetic rather than configurational cha
 nges.\nThis is a joint work with H. Waalkens and H. Broer.
LOCATION:GR A3 30 
STATUS:CONFIRMED
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