Structurally stable diffeomorphisms are dense

On Structurally Stable Diffeomorphisms with Codimension One Expanding Attractors

We show that if a closed n-manifold Mn (n ≥ 3) admits a structurally stable diffeomorphism f with an orientable expanding attractor Ω of codimension one, then Mn is homotopy equivalent to the n-torus Tn and is homeomorphic to Tn for n 6= 4. Moreover, there are no nontrivial basic sets of f different from Ω. This allows us to classify, up to conjugacy, structurally stable diffeomorphisms having ...

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...

Stable Manifolds of Holomorphic Diffeomorphisms

Problem: Determine the complex structure of the stable manifolds of f . It is not hard to see, using f(W s p ) = W s fp, that W s p is a monotone union of balls, and this in turn implies [Br] that it is diffeomorphic to real Euclidean space. Moreover, by the contracting nature of the dynamics, one sees that the Kobayashi pseudometric of W s p vanishes identically. However, when dim(W s p ) ≥ 3,...

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...

Tying Hairs for Structurally Stable Exponentials