Rinse the turnips and greens well. Cut the greens from the turnips and chop into 2-inch pieces. Trim any straggly roots from the turnips and discard. Cut the turnips into quarters or eighths, depending on size.
In a sauté pan with a lid, heat the olive oil and butter. Add the turnips, sprinkle lightly with salt and pepper, and sauté until crisp-tender, about 5 minutes. Remove the turnips from the pan. Add the greens to the pan, along with any moisture still clinging to the leaves. Cover the pan and allow the greens to cook, stirring once or twice, until just tender, 6 to 8 minutes. Add the white wine and cook until almost all the liquid is gone. Return the turnips to the pan; cook 1 to 2 minutes to heat through. Serve immediately.