Connecting Native ios app to Salesforce1?

This is currently NOT possible in Salesforce1. This is because

A) Canvas is for integrating external web applications and mobile-web based apps (both of which have a public URL) NOT native mobile applications which are installed and run on a user's device B) Both custom Chatter publisher actions and global actions work with VF pages and Canvas apps NOT with native mobile apps

Read more here

On the other hand, if you have a hybrid app which in turn invokes VF pages, you can still expose those via Salesforce1. However, it is NOT possible for 3rd party native apps. In fact, Salesforce has published guidelines on when you should opt for building native apps vs. using the Salesforce1 app.

Here is a one way to launch native app's on Salesforce1 http://www.meetingassistantapp.com/how-to-launch-native-apps-on-salesforce1/

Please let me know if it helps!