Path and quasi-homotopy for Sobolev maps between manifolds

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Sobolev maps on manifolds: degree, approximation, lifting

In this paper, we review some basic topological properties of the space X = W s,p(M ;N), where M and N are compact Riemannian manifold without boundary. More specifically, we discuss the following questions: can one define a degree for maps in X? are smooth or not-farfrom-being-smooth maps dense in X? can one lift S1-valued maps?

stable exponentially harmonic maps between finsler manifolds

The homotopy classes of continuous maps between some non - metrizable manifolds

We prove that the homotopy classes of continuous maps R → R, where R is Alexandroff’s long ray, are in bijection with the antichains of P({1, . . . , n}). The proof uses partition properties of continuous maps R → R. We also provide a description of [X,R] for some other non-metrizable manifolds.

Growing 1D and quasi 2D unstable manifolds of maps

We present a new 1D algorithm for computing the global one-dimensional unstable manifold of a saddle point of a map. This method can be generalized to compute two-dimensional unstable man-ifolds of maps with three-dimensional state spaces. Here we present a Q2D algorithm for the special case of a quasiperiodically forced map, which allows for a substantial simpliication of the general case desc...