Dynamical systems¶

Classifications of ODEs¶

TBD

Existence and uniquess for initial value problems¶

TBD

Continuous-time dynamical systems¶

TBD

Discrete-time dynamical systems¶

Consider a set \(M\) and a function \(f: M \rightarrow M\). We denote the composition of \(f\) with itself \(n\) times by \(f^n\). A fixed point \(p \in M\) is one for which \(f(p) = p\). A periodic point of period \(n\) is a point \(p \in M\) such that \(f^n(p) = p\) for some integer \(n > 0\). The smallest such \(n\) is called the period of \(p\).