A note on periodic differential equations

Details A note on periodic differential equations A note on periodic differential equations

2009-08-19

arxiv.org/abs/0908.2833v1

Mathematics

Dynamical Systems

10 pages

Scientific paper

Let $F$ be a Banach space and $L(F)$ be the set of all its bounded linear operators. In this note, we are interested in the asymptotic behavior (recurrence and chain recurrence) of the solution of the following initial value problem \label{eqlinear} x'(t) = X(t)x(t), \qquad x(0) = x, where $x \in F$ and the map $t \mapsto X(t) \in L(F)$ is a $T$-periodic continuous curve. This asymptotic behavior is related to the asymptotic behavior of the discrete-time flow on $F$ generated by the invertible operator $g \in L(F)$ given by the associated fundamental solution at time $T$.

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