Quasi-Periodic solutions for conformally symplectic dynamical systems

CDSNS Colloquium
Monday, January 14, 2013 - 4:05pm
1 hour (actually 50 minutes)
Skiles 06
Georgia Tech and ITAM
Conformally symplectic systems send a symplectic form into a multiple of itself. They appear in mecanical systems with friction proportional to the velocity and as Euler-Lagrange equations of the time discounted actions common in economics. The  conformaly symplectic structure provides identities that we use to prove "a-posteriori" theorems that show that if we have an approximate solution which satisfies some non-degeneracy conditions, we can obtain a true solution close to the approximate one.  The  identities  used to prove the theorem, also lead   to very efficient algorithms with small storage and operation counts. We will also present implementations of the algorithms.