TY - CHAP
AB - 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.
AU - Kasten, Jens
AU - Reininghaus, Jan
AU - Reich, Wieland
AU - Scheuermann, Gerik
ED - Bremer, Peer-Timo
ED - Hotz, Ingrid
ED - Pascucci, Valerio
ED - Peikert, Ronald
ID - 10893
SN - 1612-3786
T2 - Topological Methods in Data Analysis and Visualization III
TI - Toward the extraction of saddle periodic orbits
VL - 1
ER -