Hi and yes mapping is always done first and is not evasive. its thru the mapping they decide if an ablation is needed. But they will probably get your permission to go ahead with the ablation if they find something. The mapping will be like an xray. They put multiple large patches on your back and chest. Then they with drugs try to get your heart to go into an arrythmia. If they can see some bad pathways which are causing the bad rhythm that's when they will do the ablations. The mapping part also includes a large xray type machine thats placed above you mostly over you chest.

Once they decide to do ablations then they will do this from inside your heart typically first. I have had 1 of my 8 ablations done from the outside of the heart thru the side of your chest wall but this one is very rare and usually done separate from the normal ones inside the heart.
They run a catheter up from your large arteries in your groin area usually, (but Ive heard it can be done from the neck also I never had one of those) for an ablation. once inside your heart they will with burning or freezing basically isolate the bad electrical pathway that's causing the arrythmia. there may be multiple ones to ablate is where the length of the surgery entails. Typically the last step is to try and cause an arrythmia and if they are unsuccessful then that's a great sign they got all the bad pathways. The process usually takes multiple hours and can last as long as 5 hours, one of mine did.
So I hope that's a bit of the process and please ask any questions you like.