Persistence problem of compact invariant manifold under random perturbation is considered in this dissertation. Under uniformly small random perturbation and the condition of normal hyperbolicity, the original invariant manifold persists and becomes a random invariant manifold. The random counterpart has random local stable and unstable manifolds. They could be invariantly foliated thanks to the normal hyperbolicity. Those underlie an extension of the geometric singular perturbation theory to the random case which means the slow manifold persists and becomes a random manifold so that the local global structure near the slow manifold persists under singular perturbation. A normal form for a random differential equation is obtained and this helps to prove a random version of the exchange lemma.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Li, Ji, "Persistence and Foliation Theory and their Application to Geometric Singular Perturbation" (2012). All Theses and Dissertations. 3584.
Random dynamical system, Random manifold, Singular perturbation