We have two image viewers that are capable of displaying galleries on mobile devices: SimpleViewer and Juicebox.
Juicebox is an HTML image viewer whereas SimpleViewer is a Flash image viewer with a Mobile fallback for mobile devices and browsers which do not have Adobe Flash Player installed and enabled.
As such, Juicebox is much more configurable than the Mobile Player in SimpleViewer (which has only a few options compared to the Flash Player).
For more details on the differences between SimpleViewer and Juicebox, please see this SimpleViewer news article.
However, neither of these viewers would be able to replicate the layout of an AutoViewer gallery.
Both SimpleViewer and Juicebox are based around the concept of a grid of thumbnails and a single main image.
The closest you would be able to get would be to use Juicebox-Pro, hide the thumbnails (by setting showLargeThumbs="FALSE", showSmallThumbs="FALSE" and showThumbsButton="FALSE") and set imageTransitionType="SLIDE".
Demos to see what can be done with Juicebox-Lite and Juicebox-Pro can be found here.
SimpleViewer Support Team