The 11-horse field for the July 17 American Derby is a striking personification of the problems that have forced Arlington International Racecourse to the brink of extinction. Three of the Derby entries, including the favorite, were last seen contesting the Mystic Lake Derby at Canterbury Park in Minnesota. And two of those are based at Arlington, where purse cutbacks and an uncertain future have turned the facility into a virtual training center for some horsemen targeting out-of-town events.