I don't think there is Dred.
Every time the US and S. Korea hold exercises, N. Korea calls it an act of war.
My co-worker farted and I called THAT an act of war.
The US has sponsored free trade agreements with both north and south america, and Hugo Chavez of Venezuela considers that an act of war.
During the cold war, a U-2 was shot down over Russia and that was not an act of war. Just a little while ago, China forced down a US spy plane over international waters, and detained the crew and the aircraft. That was not an act of war either, even though China accused the US of using one of our uber-spyplanes to destroy a fighter plane, killing the pilot in an act of imperialist aggression after a fierce and heroic aerial battle.
Millions of Mexicans have entered the US without permission, increasing crime rates, overloading social services, and costing billions of dollars, and armed mexican police and military forces routinely cross into the US, but none of that is considered an act of war.
A couple of US police inadvertently entered Mexico while pursuing drug smugglers, and some politicians in Mexico called it a violation of national soverignty. Typically, repeated violations are considered acts of war but they don't quite have enough Mexicans in Calif or TX yet so they'll hold off on declaring war for another few years.
It all depends on whatever the government decides is worth getting all worked up about. In general, you'd think that sending armed troops into another country and shooting up the place would be a safe standard, but even that isn't the usual trigger for war.