Goal of this exercise is to sync the iphone calendar with a calendar application I use on my linux desktop. As I have multiple desktops, all should be synchronized without much effort.

 The path I took was that I used google calendar as there are my sync application that can sync betweeen in and multiple applications. For me, I'm now using the thunderbird Lightning Add-On (or: extension) to show the calendar.

This website describes the iphone <-> google calendar syncing, but you never know how long it will still be there: 

http://www.ianfernando.com/2008/sync-google-calendar-with-iphone-3g/

 And this is the website that describes the thunderbird-lighting and Google Calendar syncing:

 http://www.ianfernando.com/2008/syncing-google-calendar-to-be-more-productive/

So you need:

• A google account with google calendar enabled.
• Thunderbird
• Thunderbird-extension: Lightning (e.g. 0.9, although 0.8 worked as well). Make sure that  for 64-bit, you download a special version
• Provider for Google Calendar extension (Version 0.5 I now use)
• Sign-up for an account on www.nuevasync.com. Sync your iphone with it via A Microsoft Exchange Mail account in the "Settings / Mail Contacts Calendar" menu item. Make sure you only enable Calendar syncing, not Contacts and Mail (I use something else for sync-ing your contacts for free).