Prospective PhD-How to keep in touch with potential PhD supervisor
I fear that "close contact" is probably too much to hope for. Academics are very busy and it is rarely possible to devote a lot of time to prospective students. Close contact (hopefully) comes once you are their student, but usually not before. The best thing to do would be to see if conversation grows organically. Thank them for their email and recommendations now and let them know you are applying. Meanwhile, get in contact with them if you have something kind to say, interesting to report or important to ask: that you are coming for a visit and would like to meet, that you have finished all the suggested readings and wonder if they might have more recommendations on another subject, to congratulate them on a new publication, etc. 

Don't be offended, however, if you do not get much response to these. Like I said, we don't have much spare time for such correspondence before you are a student.