On orbits of homeomorphisms

Transfers and Periodic Orbits of Homeomorphisms

Bo Ju Jiang applied Neilsen theory to the study of periodic orbits of a homeomorphism. His method employs a certain loop in the mapping torus of the homeomorphism. Our interest concerns the persistence of periodic orbits in parameterized families of homeomorphisms. This leads us to consider fibre bundles and equivariant maps, which gives us a nice point of view.

Monotone Periodic Orbits for Torus Homeomorphisms

Let f be a homeomorphism of the torus isotopic to the identity and suppose that there exists a periodic orbit with a non-zero rotation vector ( q , r q ). Then f has a topologically monotone periodic orbit with the same

Component Orbits under Pointwise Recurrent Homeomorphisms

Turning Numbers for Periodic Orbits of Disk Homeomorphisms

We study braid types of periodic orbits of orientation preserving disk homeomorphisms. If the orbit has period n, we consider the closure of the nth power of the corresponding braid and call linking numbers of the pairs of its components turning numbers. They are easy to compute and turn out to be very useful in the problem of classification of braid types, especially for small n.

Periodic Orbits and Homoclinic Loops for Surface Homeomorphisms

Let p be a saddle fixed point for an orientation-preserving surface diffeomorphism f , admitting a homoclinic point p. Let V be an open 2-cell bounded by a simple loop formed by two arcs joining p to p, lying respectively in the stable and unstable curves at p. It is shown that f |V has fixed point index ρ ∈ {1, 2} where ρ depends only on the geometry of V near p. More generally, for every n ≥ ...