Cleveland, Jacob, authorPatel, Amit, advisorKing, Emily, committee memberDineen, Mark, committee member2025-06-022025-06-022025https://hdl.handle.net/10217/240913We introduce a novel method for extracting persistent topological descriptions of discrete dynamical systems from finite samples in the form of generalized persistence diagrams. These persistence diagrams are decorated with eigenvalues of linear maps associated to a certain local system called the persistent local system. We also prove the stability of our method and provide an example of recovering the induced map on homology from a finite sample.born digitalmasters thesesengCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.Bottleneck distancefundamental grouppersistent homologydynamical systemsalgebraic topologylocal systemText