Numerical Computation and Continuation of Invariant Manifolds Connecting Fixed Points

Numerical continuation of normally hyperbolic invariant manifolds

This paper deals with the numerical continuation of invariant manifolds regardless of the restricted dynamics. Common examples of such manifolds include limit sets, codimension 1 manifolds separating basins of attraction (separatrices), stable/unstable/centre manifolds, nested hierarchies of attracting manifolds in dissipative systems and manifolds appearing in bifurcations. The approach is bas...

Invariant manifolds near hyperbolic fixed points

In these notes we discuss obstructions to the existence of local invariant manifolds in some smoothness class, near hyperbolic fixed points of diffeomorphisms. We present an elementary construction for continuously differentiable invariant manifolds, that are not necessarily normally hyperbolic, near attracting fixed points. The analogous theory for invariant manifolds near hyperbolic equilbria...

Numerical Continuation , and Computation Ofnormal Forms

Computation of nonautonomous invariant and inertial manifolds

We derive a numerical scheme to compute invariant manifolds for timevariant discrete dynamical systems, i.e., nonautonomous difference equations. Our universally applicable method is based on a truncated Lyapunov-Perron operator and computes invariant manifolds using a system of nonlinear algebraic equations which can be solved both locally using (nonsmooth) inexact Newton, and globally using c...

FIXED POINTS OF UNITARY Z/p -MANIFOLDS

Let G = Z/ps ( p an odd prime). We show that restricting the local representations in a unitary G-manifold M with isolated fixed points results in severe restrictions on the number of fixed points (counted with the sign of their orientation), paralleling results obtained by Conner and Floyd in the case G = Z/p . Specifically, the number of noncancelling fixed points is either zero or divisible ...