Where did captain jack aubery pursue the french privateer acheron in master and commander?

In "Master and Commander: The Far Side of the World," Captain Jack Aubrey pursues the French privateer Acheron primarily in the waters around South America, particularly near the Galápagos Islands. The chase takes them across the Pacific Ocean, showcasing naval tactics and the challenges of maritime warfare during the Napoleonic Wars. Aubrey's pursuit is driven by a desire to protect British interests and assert naval dominance.