(1) Returning from the North Pole, the traveller wrote a book about his experience and had it published the following year.

填现在分词returning 作时间状语,相当于连词as soon as +he returned或者when he returend，即下面的句子：

As soon as he returned from the North Pole, the traveller wrote a book about his experience and had it published the following year.

The traveller wrote a book about his experience and had it published the following year as soon as he returned from the North Pole,

(2) Having returned from the North Pole, the traveller wrote a book about his experience and had it published the following year.

填现在分词Having returned 作时间状语,相当于连词after he had returned，即下面的句子：

After he had returned from the North Pole, the traveller wrote a book about his experience and had it published the following year.

(1) 现在分词完成体作时间状语表示，分词动作与后面句子语动词动作有相当长的一段时间间隔。

(2 )现在分词一般体作时间状语表示，分词动作与后面句子谓语动词动作是紧跟着发生的或者一前一后的发生。中间的时间间隔不长。

总结：根据句子意思：很显然是从北极回来后，写书的动作就紧跟着发生了，属于紧跟其后发生的动作，所以用现在分词一般体，不用完成体作时间状语。