How did england acquire the dutch colony that separated its other colonies?

The Dutch, who had established themselves in what is now New York, from 1609 to 1664, lost their colony, called New Holland, during the Second Anglo-Dutch War, conquered by the English. The Anglo-Dutch wars were disputed to decide who had the most dominant naval power. In 1664, both the Dutch and the English would go to war, while King Charles of England gave James, Duke of York, great territories of America, which included the colony of New Holland. James, the king's brother, assembled a small fleet that departed for the capital of the Dutch colony, New Amsterdam. When it arrived, General Stuyvesant, without any army to defend the capital of the colony, delivered the whole Dutch colony, to the British without fighting. In this way it would become the property of the English, the Dutch colony in the seventeenth century.