Fixed point index in symmetric products

Fixed Point Index in Symmetric Products

Let U be an open subset of a locally compact metric ANR X and let f : U → X be a continuous map. In this paper we study the fixed point index of the map that f induces in the n-symmetric product of X, Fn(X). This index can detect the existence of periodic orbits of period ≤ n of f , and it can be used to obtain the Euler characteristic of the n-symmetric product of a manifold X, χ(Fn(X)). We co...

Retracts, fixed point index and differential equations

Some problems in differential equations evolve towards Topology from an analytical origin. Two such problems will be discussed: the existence of solutions asymptotic to the equilibrium and the stability of closed orbits of Hamiltonian systems. The theory of retracts and the fixed point index have become useful tools in the study of these questions. Retractos, ı́ndice de punto fijo y ecuaciones d...

Fixed Point Index for Composite Type Maps

An index theory is presented for compact absorbing contractive Jc or SJc maps and several new fixed point theorems are given for such maps. AMS(MOS) subject classification: 47H10

On Coincidence and Fixed-Point Theorems in Symmetric Spaces

Super-Relational Fixed Point Property and Products in Ordered Sets

Super-relational fixed point property for ordered sets is formulated. It is weaker than the strengthened fixed point property and stronger than the product property. It is a long-standing problem whether every ordered set with the fixed point property has the product property. Several attempts have been made which solved the problem for some important classes of ordered sets. What is known may ...