DOHA, Qatar — Qatar is smaller than Connecticut, and its native population, at 225,000, wouldn’t fill Cairo’s bigger neighborhoods. But for a country that inspires equal parts irritation and admiration, here is its résumé, so far, in the Arab revolts: It has proved decisive in isolating Syria’s leader, helped topple Libya’s, offered itself as a mediator in Yemen and counts Tunisia’s most powerful figure as a friend.

This thumb-shaped spit of sand on the Persian Gulf has emerged as the most dynamic Arab country in the tumult realigning the region. Its intentions remain murky to its neighbors and even allies — some say Qatar has a Napoleon complex, others say it has an Islamist agenda. But its clout is a lesson in what can be gained with some of the world’s largest gas reserves, the region’s most influential news network in Al Jazeera, an array of contacts (many with an Islamist bent), and policy-making in an absolute monarchy vested in the hands of one man, its emir, Sheik Hamad bin Khalifa al-Thani.

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