Persia had included a couple of hundred Greek city-states in its province in Asia Minor. The cities were under local Greek government with a Persian provincial governor as was usual throughout the Empire.
These city-states were colonised by the cities in mainland Greece, and these mother-cities often interfered on the side of the daughter cities.
When the cities revolted from 499 BCE Athens and Eretria sent an expedition to help Miletus and overdid it by burning down the Persian provincial capital of Sardis. The Persian king Darius I resolved to punish them and instal a friendly government to keep them under control, and sent an expedition in 490 BCE which captured and enslaved Eretria, but failed against Athens at the battle of Marathon.
The Persian king realised that to stop this interference in his empire he would have to bring all of mainland Greece into his empire, creating an ethnic frontier. He died before he could bring this to fruition but his son Xerxes I took up the task and sent a combined naval and military force to Greece in 480 BCE, first paving the way by coercing and bribing the states of northern Greece to join him.
The invasion failed, turned back at the naval Battle of Salamis and the land battles of Plataia and Mycale. The war went on until 449 BCE when a peace was arranged.
Persia had included the Greek city-states in Asia Minor in its empire. These cities revolted, the other Greek cities gave them support. Persia then tried to keep them quiet by absorbing them into its empire.
It was not rivalry but a search for peace which brought them into conflict with Greek city-states which wanted to retain their independance and fight each other as they pleased.
It did not. The Persian War finished two decades before the outbreak of the Peloponnesian War.
The scramble for the natural resources is usually one of the events that lead to the outbreak of the war.
Darius I led the Persians in the First Persian War. Xerxes I led them in the Second.
Militarism:)
Militarism.
By the Persian king Xerxes.
Sparta and Athens were allies against Persia in the Persian War.
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Poland
The commanders appointed by the Persian kings and by the Greek city-states.
The Ionian Revolt
Darius I.