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.
Support by DGAPA-UNAM, PAPIIT IA 102818
First Day, August 1st
Video
1, Video
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 1, Video
2
Jay Mireles-James
Slides
day 2
J.P. Lessard
delayed_vdP.zip
delay_equations.pdf
Third Day, August 3rd
Video
1, Video
2
Jay Mireles-James
AMS notes
J.P. Lessard
Slides day 3