In this paper, we formulate and prove the existence theorem ofinvariant tori which persist under nonlinear perturbations in some three-dimensional measure-preserving mappings.
With the aid of a normal form of a family of measure-preserving mappings in dimension 3, which is deduced in this paper, we prove that there are periodically invariant curves which survive the nonlinear perturbations in the generic case.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.