Algorithms Converting Streamline Topologies for 2D Hamiltonian Vector Fields Using Reeb Graphs and Persistent Homology

Abstract

Abstract. Sakajo and Yokoyama have shown that any streamline topology for a 2D Hamiltonian vector field is uniquely represented by a sequence of letters. Although a conversion algorithm has been provided conceptually in these papers, its real implementation is difficult, since we need to identify a component of streamline topologies visually. In this paper, we realize a new procedure implementable to the conversion algorithm on computers through Reeb graph representations of Hamiltonian functions and extraction of specific streamline topologies using persistent homology.