Structurally Stable Quadratic Foliations

Quadratic Differentials and Foliations

This paper concerns the interplay between the complex structure of a Riemann surface and the essentially Euclidean geometry induced by a quadratic differential. One aspect of this geometry is the " trajectory structure" of a quadratic differential which has long played a central role in Teichmfiller theory starting with Teichmiiller's proof of the existence and uniqueness of extremal maps. Ahlf...

Structurally stable heteroclinic cycles

This paper describes a previously undocumented phenomenon in dynamical systems theory; namely, the occurrence of heteroclinic cycles that are structurally stable within the space of C vector fields equivariant with respect to a symmetry group. In the space X(M) of C vector fields on a manifold M, there is a residual set of vector fields having no trajectories joining saddle points with stable m...

On Stable Quadratic Polynomials

We recall that a polynomial f(X) ∈ K[X] over a field K is called stable if all its iterates are irreducible over K. We show that almost all monic quadratic polynomials f(X) ∈ Z[X] are stable over Q. We also show that the presence of squares in so-called critical orbits of a quadratic polynomial f(X) ∈ Z[X] can be detected by a finite algorithm; this property is closely related to the stability ...

Tying Hairs for Structurally Stable Exponentials

How structurally stable are global socioeconomic systems?

The stability analysis of socioeconomic systems has been centred on answering whether small perturbations when a system is in a given quantitative state will push the system permanently to a different quantitative state. However, typically the quantitative state of socioeconomic systems is subject to constant change. Therefore, a key stability question that has been under-investigated is how st...