For an area-preserving twist map F of a finite annulus, we obtain “quasi-foliations” of the annulus by one-sided-F -invariant graphs of functions that are either continuous (in which case the graph is a fully invariant curve) or have countably many jump discontinuities. For each of the one-sided-invariant graphs there is a well defined (one-sided) rotation number and all the numbers between the...

We prove that every postcritically finite rational map f:Cˆ→Cˆ admits an fn-invariant and connected graph containing the postcritical set of f as n is large enough.

Prior constraints are imposed upon a learning problem in the form of distance measures. Prototypical 2-D point sets and graphs are learned by clustering with point matching and graph matching distance measures. The point matching distance measure is approx. invariant under affine transformations translation, rotation, scale and shear and permutations. It operates between noisy images with missi...

The paper considers spacecraft motion planning based on the use of safe positively invariant sets. In this approach, a connectivity graph is constructed between a set of forced equilibria, forming a virtual net that is centered around a nominal orbital position. The connectivity between two equilibria is determined based on safe positively invariant sets in order to guarantee that transitions b...