As I saw that some twitter users make tweets from a desktop application, I sought an application developped for my favourite operating system : Ubuntu.
And then, I discovered Gwibber. This is an open source software developped with Python. A good feature is that Gwibber can be used for several service (Twitter, Flickr …). It could be improved by adding specific twitter functions such as contact management.
Here is a link to a well-written post with screenshots that gives more details about this software :