12 citations · 21 across the 12 of their papers we have counts for
15 papers
The Szymczak Functor on the Category of Finite Sets and Finite Relations
Mateusz Przybylski, Marian Mrozek, Jim Wiseman
The Szymczak functor is a tool used to construct the Conley index for dynamical systems with discrete time. We present an algorithmizable classification of isomorphism classes in t…
Persistence of Morse decompositions over grid resolution for maps and time series
Jim Wiseman
We can approximate a continuous self-map of a compact metric space by discretizing the space into a grid. Through either the map itself or a time series, induces a multival…
A Conley-type Lyapunov function for the strong chain recurrent set
Olga Bernardi, Anna Florio, Jim Wiseman
Let be a continuous flow on a compact metric space . In this article we constructively prove the existence of a continuous Lyapunov funct…
The generalized recurrent set, explosions and Lyapunov functions
Olga Bernardi, Anna Florio, Jim Wiseman
We consider explosions in the generalized recurrent set for homeomorphisms on a compact metric space. We provide multiple examples to show that such explosions can occur, in contra…
Chain Recurrence For General Spaces
Ethan Akin, Jim Wiseman
The chain relation, due to Conley, and the strong chain relation, due to Easton, are well studied for continuous maps on compact metric spaces. Following Fathi and Pageault, we use…
Generalized Recurrence and the Nonwandering Set for Products
Jim Wiseman
For continuous maps of compact metric spaces and and for various notions of topological recurrence, we study the relationship between recurrence for and $…