Volume preservation refers to the property of a transformation or flow that maintains the volume of a given region in space. This concept is crucial in symplectic geometry, where certain transformations, such as symplectomorphisms, preserve a symplectic structure, and thus the volume defined by this structure. Volume preservation helps us understand the behavior of dynamical systems and is essential in proofs related to important theorems like Darboux's theorem and Gromov's non-squeezing theorem.
congrats on reading the definition of Volume Preservation. now let's actually learn it.