CDLab workshop
We are organizing a twoday workshop on Friday 22 and Tuesday 26 February 2019 to discuss and work on our current research problems.
Friday 22 February 2019

09:30–10:30 Sala riunioni
Francesca Scarabel: Next goal: periodic solutions.
The pseudospectral discretization of nonlinear delay equations accurately approximates equilibria and their stability. This is a short overview of the ideas that should lead to similar convergence results for periodic solutions, starting from an essential and yet nontrivial step: the approximation of the solution operators. 
10:30–11:30 Sala riunioni
Stefano Maset: About relative errors in dynamical systems.
On recent results about the propagation in time of relative errors in dynamical systems generated by either ordinary and delay differential equations. 
11:30–12:30 Sala riunioni
Alessia Andò: Two BVP formulations for periodic solutions of DDEs.
In view of computing periodic solutions of DDEs, the classic BVP formulation hides the periodicity in the righthand side of the equation. We show that this formulation is not suitable if one solves the BVP as a fixed point problem. Therefore we investigate an alternative which keeps the periodicity in the boundary condition. 
14:00–18:00 Saletta riunioni
General discussion.
Tuesday 26 February 2019

09:30–10:30 Sala riunioni
Rossana Vermiglio: TBA. 
10:30–11:30 Sala riunioni
Davide Liessi: Stability of periodic solutions of renewal equations.
Assuming the validity of two hypotheses, the Floquet theory and the principle of linearized stability for periodic solutions hold true for abstract integral equations. I present the latest work by Dimitri and me, where we prove the validity of those two hypotheses for renewal equations. In that work we also provide a detailed proof of the principle of linearized stability for abstract integral equations, whose novel idea I present as well. 
11:30–12:30 Sala riunioni
Dimitri Breda: On periodic solutions of linear periodic ODEs.
It is a classic result that a linear \(\omega\)periodic inhomogeneous ODE has an \(\omega\)periodic solution for every choice of the forcing term iff the corresponding homogeneous ODE does not (but for the trivial one). Therefore, if this homogeneous ODE has a nontrivial \(\omega\)periodic solution, then there exists a choice of the forcing term for which the inhomogeneous ODE has no \(\omega\)periodic solutions. Under this hypothesis and motivated by numerical methods, we discuss a class of inhomogeneous ODEs which does not admit an \(\omega\)periodic solution. 
14:00–18:00 Sala riunioni
General discussion.