Connection graphs
We introduce connection graphs for both continuous and discrete dynamical systems. We prove the existence of connection graphs for Morse decompositions of isolated invariant sets.
Simple connection matrices
We introduce simple connection matrices. We prove the existence of simple connection matrices for filtered differential vector spaces and Morse decompositions of compact metric spaces.
Connection matrix theory for discrete dynamical systems
In [C] and [F1] the connection matrix theory for Morse decomposition is developed in the case of continuous dynamical systems. Our purpose is to study the case of discrete time dynamical systems. The connection matrices are matrices between the homology indices of the sets in the Morse decomposition. They provide information about the structure of the Morse decomposition; in particular, they give an algebraic condition for the existence of connecting orbit set between different Morse sets.
On the homotopy equivalence of the spaces of proper and local maps
We prove that for n > 1 the space of proper maps P 0(n, k) and the space of local maps F 0(n, k) are not homotopy equivalent.
Gradient otopies of gradient local maps
We introduce various classes of local maps: gradient, gradient-like, proper etc. We prove Parusiński's theorem for otopy classes of gradient local maps.
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