Seminář o diferenciálních rovnicích se koná v pondělí 15.5.2023 od 12 hodin v posluchárně M5.

Roberta Fabbri (Mathematics and Computer Science "Ulisse Dini", University of Florence)

Some questions concerning nonautonomous linear Hamiltonian systems

Abstrakt:
In the talk the definitions and properties of the rotation number and exponential dichotomy for linear non-autonomous Hamiltonian systems are presented. Some applications to spectral theory for properly perturbed Hamiltonian systems and linear quadratic minimization problems are also presented. Finally, starting from the geometric definition of the rotation number related to the Arnold-Maslov index, some ideas on numerical computation of the Maslov index for frames, i.e., Lagrange planes generated by the solutions of the systems, are given. This is related to the spectral theory of the \(n\)-dimensional Schrödinger equation.