Also known as a trail cam or many other various names. Sometimes they can be had at extremely good prices. They're battery powered, motion detecting, and camouflaged. Get a nice high resolution photo of the perp.
On a related note, a friend of mine had his vacation house badly burglarized a month ago. A neighbor noticed it and called him. He had motion detecting cameras installed, and a week later, his phone told him motion had been detected behind his house. He looked at the live video, realized it wasn't anyone authorized to be there, and set off a loud alarm. The would-be burglar fled at the sound of the alarm. The local sheriff was called and the video sent over. The Sheriff recognized the car as belonging to a local trouble maker. The Sheriff drove over, found the car, and now had probably cause to enter. They found some of the items stolen the week before. Especially a rifle. Too bad the suspect was a convicted felon, now caught with a stolen firearm. He's now looking at serious jail time. There's still many thousands of dollars worth of missing property, but at least one of the burglars is behind bars.