Is it possible in ArcGis (from a technology/performance/… point of view) to switch projections depending on the zoom level?
For example, Is it possible when zooming at some extent to the poles, my projection to be switched from the "Miller projection" to "stereographic projection". For polar areas, a stereographic projection is best.
According to your edit, you want to
create a map (layers, featured services etc) using ArcGis for Desktop, which in turn will be used via the Javascript API in my application
This is simply not possible. When you publish a map as MapService, it takes on the projection of the Map. In ArcGIS for Desktop, there is no out of the box way to change the map's spatial reference according to the zoom level or location.
Similarly, once the Map has been published as a MapService, the native resolution of the Map Service is fixed. It cannot change according to zoom level or location.
There is an hard workaround for what you want to do.
The map and data can be requested from the MapService in various projections. You can do the changing of the projection in the API you use to draw the map. I know that none of the ArcGIS Web APIs offer this. But if you are looking at vectors, you could look into something like d3 which can change projection on the fly. The obstacle that you ar going to face here, is that, AFAIK there is no pre-existing library for showing your ArcGIS Server Data in d3. You'll have to roll your own.
