Convergence to a period one fixed point is investigated for both logistic and cubic maps. For the logistic map the relaxation to the fixed point is considered near a transcritical bifurcation while for the cubic map it is ...

In 1969 R.H. Bing asked the following question: Is there a compact two-dimensional polyhedron with the fixed point property which has even Euler characteristic? In this paper we prove that there are no spaces with these ...

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S-1 for spaces which axe fibrations over S-1 and the fiber is the torus T. For the case where the fiber is a surface with ...

We prove that for any connected compact CW-complex K there exists aspace X weak homotopy equivalent to K which has the fixed point property, that is,every continuous map X -> X has a fixed point. The result is known to be ...

Using the notion of summable dichotomy in ordinary difference equations and the contraction and Schauder fixed point theorem, we obtain the existence of bounded and periodic solutions on ℤ under quite general hypotheses ...

Rare collisions of a classical particle bouncing between two walls are studied. The dynamics is described by a two-dimensional, nonlinear and area-preserving mapping in the variables velocity and time at the instant that ...

This paper proves the existence and uniqueness of a fixed-point for local contractions without assuming the family of contraction coefficients to be uniformly bounded away from 1. More importantly it shows how this fixed-point ...

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be ...