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Published within last ten years.

Guy enters machine. Comes out; the world is slightly different. He goes home, finds another guy is living his life. "Oh my god," he realizes, "I'm in a different timeline" and tries to get back.

But copies are made of him each time. Eventually, in remote Wisconsin in winter, each believing they are the true guy, they battle the protagonist to be the one.

In one scene he is in the machine and there is a corridor with many doors. Each a different Chicago, one with excellent public transit.

Dark Matter by Blake Crouch. It involves Jason Dessen, a physics professor from Chicago, who is abducted by a version of himself from an alternate reality who wants to take over his life. As the protagonist himself describes it:

“A man of science, a physics professor, is living here in Chicago. He isn’t wildly successful like he always dreamed, but he’s happy, mostly content, and married”—I look at Daniela, thinking of how Ryan described it back at the gallery—“to the woman of his dreams. They have a son. They have a good life. One night, this guy goes to a bar to see an old friend, a college buddy who recently won a prestigious award. On the walk back, something happens. He never makes it home. He’s abducted. The events are murky, but when he finally regains his full presence of mind, he’s in a lab in South Chicago, and everything has changed. His house is different. He’s not a professor anymore. He’s no longer married to this woman."

The machine is described as like a corridor with infinitely repeating doors.

It looks like a corridor, but I think it’s actually the box repeating itself across all possible realities that share the same point in space and time.

He travels to an alternate reality with extensive public transport.

A quarter mile ahead, a series of elegant Y-shaped structures cut across the park at intervals of fifty meters.
Only as we draw near do I realize what they are.
We ride a lift up to the northbound platform and wait under the heated overhang, now forty feet above the greenway. A digital, interactive map emblazoned with Chicago Transit Authority identifies this route as the Red Line Express, linking South Chicago to Downtown.

After making it back to his own reality the protagonist eventually drives to Wisconsin to avoid alternate copies of himself.

We leave with nothing but the clothes on our backs and a bank envelope filled with cash from our emptied checking and savings accounts. Daniela puts the rental car on our credit card, but every transaction going forward will be cash-only to make us harder to track.
By midafternoon, we’re cruising through Wisconsin.