Floquet Theory and Applications

Abstract

This project is at the interface between Analysis, Natural Sciences and Modeling Theory. It deals with Floquet Theory (also re ered to as Floquet-Lyapunov theory) which is the main tool of the theory of periodic ordinary di erential systems of the form dx = A(t)x dt (1) where A(t) is an n × n matrix with periodic coe cients, and x is an unknown column n-vector function. Such systems arise in many physical and technical situations (Population growth, Astronomy, Climatology, Seismology, Chaos, Turbulence, Industrial and nancial growth, Natural resource shortening, Elasticity theory, Hydrodynamics, ... ). Floquet Theory provides Floquet multipliers of (1), of which distribution in the complex plane informs about the solvability and the stability of periodic solutions to (non)homogeneous systems of di erential equations.