Topologically crossing heteroclinic connections to invariant tori

The Genesis Trajectory and Heteroclinic Connections

Genesis will be NASA's first robotic sample return mission. The purpose of this mission is to collect solar wind samples for two years in an £ 1 halo orbit and return them to the Utah Test and Training Range {UTTR) for mid-air retrieval by helicopters. To do this, the Genesis spacecraft makes an excursion into the region around £ 2 . This transfer between £ 1 and L 2 requires no deterministic m...

Reconfiguring Smart Structures using Approximate Heteroclinic Connections

A new method is investigated to reconfigure smart structures by the technique of polynomial series, used to approximate a true heteroclinic connection between unstable equilibria in a smart structure model. We explore the use of polynomials of varying order to firstly approximate the heteroclinic connection between two equalenergy unstable equilibrium points, and then develop an inverse method ...

Topologically Left Invariant Mean on Dual Semigroup Algebras

Constructive invariant theory for tori

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Existence of Critical Invariant Tori

We consider analytic Hamiltonian systems with two degrees of freedom, and prove that every Hamiltonian on the strong local stable manifold of the renormalization group fixed point obtained in [26] has a non-differentiable golden invariant torus (conjugacy to a linear