--- res: bibo_abstract: - Saddle periodic orbits are an essential and stable part of the topological skeleton of a 3D vector field. Nevertheless, there is currently no efficient algorithm to robustly extract these features. In this chapter, we present a novel technique to extract saddle periodic orbits. Exploiting the analytic properties of such an orbit, we propose a scalar measure based on the finite-time Lyapunov exponent (FTLE) that indicates its presence. Using persistent homology, we can then extract the robust cycles of this field. These cycles thereby represent the saddle periodic orbits of the given vector field. We discuss the different existing FTLE approximation schemes regarding their applicability to this specific problem and propose an adapted version of FTLE called Normalized Velocity Separation. Finally, we evaluate our method using simple analytic vector field data.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Jens foaf_name: Kasten, Jens foaf_surname: Kasten - foaf_Person: foaf_givenName: Jan foaf_name: Reininghaus, Jan foaf_surname: Reininghaus foaf_workInfoHomepage: http://www.librecat.org/personId=4505473A-F248-11E8-B48F-1D18A9856A87 - foaf_Person: foaf_givenName: Wieland foaf_name: Reich, Wieland foaf_surname: Reich - foaf_Person: foaf_givenName: Gerik foaf_name: Scheuermann, Gerik foaf_surname: Scheuermann bibo_doi: 10.1007/978-3-319-04099-8_4 bibo_volume: 1 dct_date: 2014^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/1612-3786 - http://id.crossref.org/issn/2197-666X - http://id.crossref.org/issn/9783319040981 dct_language: eng dct_publisher: Springer@ dct_title: Toward the extraction of saddle periodic orbits@ ...