Let f be an orientation preserving homeomorphism on the circle with several break points, that is, its derivative Df has jump discontinuities at these points. We study Rauzy-Veech renormalizations of piecewise smooth homeomorphisms by considering such maps as generalized interval exchange genus one. Suppose is absolutely continuous each continuity and \(D\ln {Df}\in {\mathbb {L}}_{p}\) for some...

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.

We investigate the end spaces of infinite dual graphs. We show that there exists a natural homeomorphism between the end spaces of a graph and its dual, and that this homeomorphism maps thick ends to thick ends. Along the way, we prove that Tutte-connectivity is invariant under taking

This paper is concerned with fuzzy cellular neural networks with distributed delays. Sufficient conditions on the existence, uniqueness and global exponential stability of equilibrium point are established by using the Homeomorphism theory and applying elementary inequality 2ab ≤ a2 + b2. Moreover an example is given to illustrate results obtained. Key–Words: Fuzzy cellular neural networks, Glo...