Smooth dynamical systems as infinitesimal discrete dynamical systems

This page cannot be shown here. You can still read it on the original site — the toolbar below keeps your place in the directory.

Here I am working with nonstandard analysis in the sense of Robinson, taking an ultrapower of the real numbers and building things out of that. But in general I am going to be a bit sloppy and not worry too much about the details. Recall that a standard function is differentiable if, for every standard \(x\) and for every infinitesimal \(\epsilon\), \(f(x+\epsilon)-f(x)/\epsilon \approx a\), where…

Read on /smooth-dynamical-systems-as-infinitesimal/ ↗