Jake Gyllenhaal did not receive an Oscar nomination for portraying Adam Bell and Anthony Claire in Enemy.
We first meet Jake Gyllenhaal as Adam Bell who is a literary college professor. Gyllenhaal portrays Bell as a very reserved man. Gyllenhaal effectively sets up Adam as very closed off, and a bit depressed as he just seems to go along his life without anything special happening. Even when spending time with his girlfriend Mary (Mélanie Laurent) Gyllenhaal suggests that all Adam is doing is going through the motions. Suddenly though Adam finds a strange purpose when he sees an actor in a bit part in a film that looks just like him. Gyllenhaal is convincing in portraying Adam's curiosity stemming basically from his disinterest with his life, and Gyllenhaal is effective in portraying the enthusiasm of man who's found something to be involved in. At first Gyllenhaal shows Adam as just being interested as one might be that suddenly they have some sort of twin, and would probably want to know what exactly the explanation is. It does not take long for him to find Anthony a small time actor with a pregnant wife.
Gyllenhaal is quite good in portraying the differences of Anthony without having something specific to set them apart. Gyllenhaal though portrays Anthony as a far more easy going sort and Gyllenhaal adjusts his body language to more extroverted portraying Anthony as a man who seems to be much more comfortable with his existence than Adam is. Gyllenhaal changes his presence well to a far more aggressive sort of man who rather than drifts like Adam, clearly takes exactly what he wants when he wants it. This becomes particularly obvious that Anthony's life is not perfection either as he has not been faithful to his own wife, and seems to have no real intention to not stray again. When they finally meet together Gyllenhaal is good in portraying the conflicting attitudes of the two man as Adam seems to become racked with fear over his doppelganger, whereas Gyllenhaal portrays Anthony as kinda relishing in the idea, hinting from this first occasion that Anthony sees some potential for himself in this man that looks like him.
After the meeting Adam retreats back into himself seemingly crumbling with this world bending revelation. Anthony on the other hand sees it as a chance for an affair, with Adam's girlfriend, which he likely believes will stop him from being caught because he'll simply be Adam. Gyllenhaal does have a great scene with himself as he brings the forcefulness of Anthony as he imposes his will against Adam, who Gyllenhaal cowers as still unsure and confused over his own reality because of Anthony's existence. So they both go off as each other. Anthony goes off perfectly as Adam, although as himself since he only wants to impersonate Anthony for the most basic of satisfaction. Adam on the other hand only suffers from the concept of switching and does not relish at all in attempting to emulate Anthony's behavior with Adam's wife. The twist ends up being that Anthony is caught, due to a mark from his wedding band giving him away, and Adam connects with Anthony's wife since they are both being abused by Anthony.
I really can't complain about Jake Gyllenhaal's performance here at all. He does a fine job of realizing both Adam and Anthony in the way they connect, but also as two separate individuals. My only reservations comes from the film itself which never makes much of a use of the idea of the doppelganger. I will admit I lost my patience with the film as the film cared much more about Villeneuve's attempts to emulate David Lynch's camera movements, and weird imagery, which Villeneuve better just leave to Lynch because he's just not that good at it. Jake Gyllenhaal simply does not have the material to turn Adam and Anthony into that memorable of characters. I have no complaints in regard to Gyllenhaal's own work though because he is as believable as he can be in the role and tries hard to make something out of the material, but it's just a bit too thin for him to make them come to life as they should. I'd love to see Gyllenhaal plays twins again as he does prove himself quite capable in such a role, I wish it was for a superior film though.