In Cocoa, is there a notification i can register for, that informs me, when a new day begins - at 00h:00min:01s in the morning?
There's no notification that I know of. You can get a timer to fire whenever a new day begins like so:
[[NSTimer alloc] initWithFireDate:midnight
interval:60 * 60 * 24 //one day, in seconds
target:someObj
selector:@selector(someSelector)
userInfo:nil
repeats:YES];
The trick is getting an NSDate set to midnight. Check the Date and Time Programming Guide for how to do that with date components and the like.
EDIT: see this question for how to get the midnight NSDate.