Triremes were the dreadnoughts of the classical era. They were expensive and required a great deal of maritime expertise, not to mention social class cohesion, in order to be effective in battle. The Athenian democratic political structure led to Athens dominating the seas until losses in the latter part of the Peloponessian War meant a degradation of the quantitative and qualitative advantages they held over the Spartans.

Trireme from didactylos47's photostream

Equally important was the logistical structure supporting the triremes. This is true for most military endeavours; American hegemony currently is based upon American dominance of logistics such that their forces can maintain a high tempo indefinitely. This was also true of the British military in their hay day. Triremes were short range weapons heavily reliant on human labor at the oars. Consequently they needed constant water and food provisioning. (more)

During the Athenian Sicilian campaign the cavalry of the Syracuse became the dominant weapon on the battlefield, stifling the forty thousand strong Athenian hoplites from gaining the advantage in the field. The Athenians in return raised their own cavalry and sent it to Sicily. They weren't the knights of medieval times though, they were small ponies, approximately four and half feet tall, and they lacked stirrups. Hardly frightening, except the Greeks of that time were tiny. Hanson writes:

These tiny mounts, mostly stallions, were only partialled protected with light cloth padding over the face, thighs and chest, and harder to ride than geldings.

It was hard to train riders to control the stallions as well as handle a spear and blade in battle. (more)

America is the current global hegemon, so it is always possible to make analogies with the US and prior super-powers such as Britain, Rome, and even Athens. Victor Davis Hanson looks at the analogies between America and Athens in A War Like No Other. One of the curiosities of Sparta was that they would promise to bring tyranny to the states they liberated from Athenian democracy. Tyranny back then being a legitimate government form while democracy was the radical, liberal and egalitarian form of subversiveness. (more)