Hello,
It is possible and takes quite the customization:
1) Add 2 DatePicker objects; the first one call it 'Today's Date' and check the 'Use Today's Date/Time' checkbox as the default, the second one call it 'Date' and don't do anything to it. Make sure they are hidden (if you want)
2) Go to Advanced and on screen load you will add 2 actions: 1. Date Add with Starting date being pulled from screen form 'Today's Date', make the date/time interval Days, then set the Number to add as the number of days you want to see (so if you want to display activities coming within the week, put in 7), give your action result a name, 'getWeek' I guess is a good name.. 2. Enter your action result into the Date Object - use enter value onto screen
3) Edit the Activity grid and on the filters screen, create a new filter view (we will make this view display activities coming in the next week). Copy the filters that are in the 'My Active Occurences In The Future', you will add a new filter from DueDateStart that will be Less than or equal to value on screen which will be Date.
4) save and publish
This should show you all the activities that are coming in however number of days you specify filtering your recourring activities, BUT it will not show you more than that. You could however completely hide recurring activities, but I'm not sure if you want to do that. If you want to show everything after the days specified except for the recurring activites is going to be very difficult due to limitations in the platform; however, it does make sense theoretically if you use advanced SQL overrides.
extra - you could get fancy and make the Date object visible and make it dynamic so that you see in the future as much as you specify. You can do that by assigning the number of days to an action result and pull it from your filter view.
Hope that was helpful,
Marwan