Topological invariants, multivalued maps and computer assisted proofs in dynamics

We introduce the concept of inheritable properties of multivalued maps, and show how this concept, when combined with interval arithmetic and representable multivalued approximations, may be used in adapting topological methods to computer assisted proofs in dynamics. As our first example, we propose a simple geometric criterion for chaos. A more sophisticated example is the Conley index theory. We show how the computation for the Conley index for multivalued representable maps may be reduced to a finite computation. This reduction was used in the computer assisted proof of chaos in the Lorenz equations represented in [1].