Computer assisted proofs in Nonlinear Dynamics

Enviamos una cordial invitación al curso de posgrado de tres días que imparten los profesores Jean-Philippe Lessard (McGill University) y Jason Mireles-James (Florida Atlantic Univesity) en el IIMAS. El curso está abierto a la comunidad científica en general y dirigido a estudiantes de posgrado, posdocs y profesores interesados en pruebas asistidas por computadora en ecuaciones diferenciales.

El curso se impartirá el 1, 2 de agosto de 4 a 7 pm y el 3 de agosto de 4 a 6 pm.

Salón 201, edificio anexo del IIMAS


CURSO

Computer assisted proofs in Nonlinear Dynamics

Many problems in differential equations can be reduced to questions about the the zeros of some (possibly infinite dimensional) nonlinear function. Examples include equilibrium solutions, periodic solutions, their attached invariant manifolds, connecting orbits, invariant tori, etcetera. In many applications, especially when there are no small parameters, the resulting nonlinear equations are too difficult to solve by hand, and we resort to numerical simulations to better understand the problem.

The main question addressed in this workshop is this: suppose we have computed a good numerical approximation -- can we establish the existence of a true solution nearby? Combining tools from functional analysis, complex analysis, numerical analysis, and interval computing, we see that for many of the problems mentioned above the answer is yes. Over the three days we will give a broad and example driven overview of the field of validated numerics.


First Day, August 1st

Video 1Video 2

Jay Mireles-James
Slides day 1

J.P. Lessard
Laplace_Beltrami.zip
radially_symmetric_solutions.pdf
review_notices.pdf


Second Day, August 2nd

Video 1Video 2

Jay Mireles-James
Slides day 2

J.P. Lessard
delayed_vdP.zip
delay_equations.pdf


Third Day, August 3rd

Video 1Video 2

Jay Mireles-James
AMS notes

J.P. Lessard
Slides day 3