Rinse and dry the salmon and put to one side. Peel, core and thinly slice the apples. Thickly butter an ovenproof dish or cast-iron frying pan, and put the apple slices in it, together with the sugar and white wine. Cook in a preheated oven at 180°C / 350°F / Mark 4 for 10 minutes, and then remove and keep the apples warm.
To make the sauce, decant the apple cooking juices into a saucepan. Peel the zest from the limes and reserve it. Squeeze the fruit, and add 2½ fl oz / 70 ml. of the juice to the pan. Cook the liquid over a low heat to reduce slightly, then gradually add most of the remaining butter, a little at a time, whisking it to blend and emulsify the ingredients. Keep the butter sauce warm while you quickly cook the salmon. Lightly season the fillets, and dust with flour. Fry them in the remaining butter for about 5 minutes. Arrange the apple slices on plates with the salmon on top, and spoon over the sauce. Garnish with the reserved lime zest, shredded.