Approximating stable and unstable manifolds in experiments.

Smooth Stable and Unstable Manifolds for Stochastic Partial Differential Equations

Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of stochastic partial differential equations. We first show the existence of Lipschitz continuous stable and unstable manifolds by the Lyapunov-Perron’s method. Th...

The Intersection Angles between N-Dimensional Stable and Unstable Manifolds in 2N-Dimensional Symplectic Mappings

We asymptotically compute the intersection angles between N -dimensional stable and unstable manifolds in 2N -dimensional symplectic mappings. There exist particular 1-dimensional stable and unstable sub-manifolds which experience exponentially small splitting of separatrix in our models. We show that the angle between the sub-manifolds is exponentially small with respect to the perturbation pa...

Exponentially small oscillation of 2-dimensional stable and unstable manifolds in 4-dimensional symplectic mappings

Homoclinic bifurcation of 4-dimensional symplectic mappings is asymptotically studied. We construct the 2-dimensional stable and unstable manifolds near the submanifolds which experience exponentially small splitting, and successfully obtain exponentially small oscillating terms in the 2-dimensional manifolds. ∗ E-mail address: [email protected] 1 typeset using PTPTEX.sty <ver...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Stable and Unstable Manifolds for Quasilinear Parabolic Problems with Fully Nonlinear Dynamical Boundary Conditions

We develop a wellposedness and regularity theory for a large class of quasilinear parabolic problems with fully nonlinear dynamical boundary conditions. Moreover, we construct and investigate stable and unstable local invariant manifolds near a given equilibrium. In a companion paper we treat center, center–stable and center–unstable manifolds for such problems and investigate their stability p...