UC Santa Cruz

Cineli, Ginzburg, and Gurel recently defined a new quantity, called the barcode entropy, which is calculated using barcodes of a Floer-Novikov complex, similar to barcodes arising in persistence homology and Morse theory. They were able to relate this to the classical topological entropy, a number that quantifies the complexity of the orbits of a map. This quantity is of high interest in dynamics as its positivity indicates that the orbits of a dynamical system are more likely chaotic. They were able to define barcode entropy and find a connection between this quantity and topological entropy for the case when the map in question is a Hamiltonian diffeomorphism. In this dissertation, we extend their results to the case when the map is more generally just a symplectomorphism isotopic to the identity.