Index pairs and the fixed point index for semidynamical systems with discrete time

Weak Index Pairs and the Conley Index for Discrete Multivalued Dynamical Systems

Motivation to revisit the Conley index theory for discrete multivalued dynamical systems stems from the needs of broader real applications, in particular in sampled dynamics or in combinatorial dynamics. The new construction of the index in [B. Batko and M. Mrozek, SIAM J. Applied Dynamical Systems, 15(2016), pp. 1143-1162] based on weak index pairs, under the circumstances of the absence of in...

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

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...

THE FIXED POINT INDEX AND ASYMPTOTIC FIXED POINT THEOREMS FOR ft-SET-CONTRACTIONS

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...