Her motive is bread crumbs. She put her toe in the water to see how you would react. She is looking for validation, seeing if you are still on the hook. She wants to see if she still owns you, And also looking to see if she can stir old feelings and get back in your head.
If you "catch up, or contact her in a month," this will stroke her ego and give her what she is looking for.
If i were you i would just carry on with my life. If you happen to be in her city, call her friend. Meet her friend. Go for coffee with the friend. Ignore the ex. If the ex happens to "accidently" call again treat her with absolute indifference.