Normal forms for difference and differential systems (Q2114391)

There are two ways to bridge difference and differential equations. One is the suspension, which makes diffeomorphisms as Poincaré recurrence maps of periodic differential systems. The second is the Euler's approximation, depending on a real parameter \(\mu\), which is well known for its wide applications in numerical computations for vector fields. The authors investigate parametrized difference systems, which can yield normal forms of vector fields and diffeomorphisms together. So the main purpose of this work is to investigate the behavior of normal forms with respect to the \(\mu\)-approximation. Very roughly speaking, the main result is that the normal forms of periodic difference systems and differential systems can be achieved uniformly.