Pomegranate Martini. Stir or Shaken?

For Simple Syrup
2 Bring sugar and water to a small pan and simmer until the sugar is dissolved. Chill until ready to use.
For Martini
5 In a large decanter add the pomegranate juice, vodka, lemon juice and simple syrup. Stir well. Refrigerate until ready to use.
6 In a martini shaker add the crushed ice and ½ per glass of the martini mix. Shake well and pour the pomegranate mix into a martini glass, with no ice.Add the spring of mint and the fine lemon’s strips.