Strong Conley index over a phase space

The Conley index over a phase space for flows

We construct the Conley index over a phase space for flows. Our definition is an alternative for the Conley index over a base defined in [5]. We also compare it to other Conley-type indices and prove its continuation property.

Strong Phase-Space Semiclassical Asymptotics

Wigner and Husimi transforms have long been used for the phasespace reformulation of Schrödinger-type equations, and the study of the corresponding semiclassical limits. Most of the existing results provide approximations in appropriate weak topologies. In this work we are concerned with semiclassical limits in the strong topology, i.e. approximation of Wigner functions by solutions of the Liou...

Shift Equivalence and the Conley Index

In this paper we introduce filtration pairs for isolated invariant sets of continuous maps. We prove the existence of filtration pairs and show that, up to shift equivalence, the induced map on the corresponding pointed space is an invariant of the isolated invariant set. Moreover, the maps defining the shift equivalence can be chosen canonically. Lastly, we define partially ordered Morse decom...

Efficient Automation of Index Pairs in Computational Conley Index Theory

We present new methods of automating the construction of index pairs, essential ingredients of discrete Conley index theory. These new algorithms are further steps in the direction of automating computer-assisted proofs of semiconjugacies from a map on a manifold to a subshift of finite type. We apply these new algorithms to the standard map at different values of the perturbative parameter ε a...

The Conley Index and Rigorous Numerics